On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3
Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifyi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Şenyurt, Süleyman [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Basel 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Advances in applied Clifford algebras - Cham (ZG) : Springer International Publishing AG, 1997, 25(2015), 4 vom: 14. Feb., Seite 977-988 |
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| Übergeordnetes Werk: |
volume:25 ; year:2015 ; number:4 ; day:14 ; month:02 ; pages:977-988 |
| Links: |
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| DOI / URN: |
10.1007/s00006-015-0535-z |
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| Katalog-ID: |
SPR000085758 |
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| 100 | 1 | |a Şenyurt, Süleyman |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 |
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| 520 | |a Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. | ||
| 650 | 4 | |a Darboux vector |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a involute curve |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a ruled surface |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a helix |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Kılıçoğlu, Şeyda |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Advances in applied Clifford algebras |d Cham (ZG) : Springer International Publishing AG, 1997 |g 25(2015), 4 vom: 14. Feb., Seite 977-988 |w (DE-627)507183274 |w (DE-600)2220151-8 |x 1661-4909 |7 nnns |
| 773 | 1 | 8 | |g volume:25 |g year:2015 |g number:4 |g day:14 |g month:02 |g pages:977-988 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00006-015-0535-z |z lizenzpflichtig |3 Volltext |
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10.1007/s00006-015-0535-z doi (DE-627)SPR000085758 (SPR)s00006-015-0535-z-e DE-627 ger DE-627 rakwb eng Şenyurt, Süleyman verfasserin aut On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. Darboux vector (dpeaa)DE-He213 involute curve (dpeaa)DE-He213 ruled surface (dpeaa)DE-He213 helix (dpeaa)DE-He213 Kılıçoğlu, Şeyda aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 25(2015), 4 vom: 14. Feb., Seite 977-988 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:25 year:2015 number:4 day:14 month:02 pages:977-988 https://dx.doi.org/10.1007/s00006-015-0535-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 14 02 977-988 |
| spelling |
10.1007/s00006-015-0535-z doi (DE-627)SPR000085758 (SPR)s00006-015-0535-z-e DE-627 ger DE-627 rakwb eng Şenyurt, Süleyman verfasserin aut On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. Darboux vector (dpeaa)DE-He213 involute curve (dpeaa)DE-He213 ruled surface (dpeaa)DE-He213 helix (dpeaa)DE-He213 Kılıçoğlu, Şeyda aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 25(2015), 4 vom: 14. Feb., Seite 977-988 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:25 year:2015 number:4 day:14 month:02 pages:977-988 https://dx.doi.org/10.1007/s00006-015-0535-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 14 02 977-988 |
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10.1007/s00006-015-0535-z doi (DE-627)SPR000085758 (SPR)s00006-015-0535-z-e DE-627 ger DE-627 rakwb eng Şenyurt, Süleyman verfasserin aut On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. Darboux vector (dpeaa)DE-He213 involute curve (dpeaa)DE-He213 ruled surface (dpeaa)DE-He213 helix (dpeaa)DE-He213 Kılıçoğlu, Şeyda aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 25(2015), 4 vom: 14. Feb., Seite 977-988 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:25 year:2015 number:4 day:14 month:02 pages:977-988 https://dx.doi.org/10.1007/s00006-015-0535-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 14 02 977-988 |
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10.1007/s00006-015-0535-z doi (DE-627)SPR000085758 (SPR)s00006-015-0535-z-e DE-627 ger DE-627 rakwb eng Şenyurt, Süleyman verfasserin aut On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. Darboux vector (dpeaa)DE-He213 involute curve (dpeaa)DE-He213 ruled surface (dpeaa)DE-He213 helix (dpeaa)DE-He213 Kılıçoğlu, Şeyda aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 25(2015), 4 vom: 14. Feb., Seite 977-988 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:25 year:2015 number:4 day:14 month:02 pages:977-988 https://dx.doi.org/10.1007/s00006-015-0535-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 14 02 977-988 |
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10.1007/s00006-015-0535-z doi (DE-627)SPR000085758 (SPR)s00006-015-0535-z-e DE-627 ger DE-627 rakwb eng Şenyurt, Süleyman verfasserin aut On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. Darboux vector (dpeaa)DE-He213 involute curve (dpeaa)DE-He213 ruled surface (dpeaa)DE-He213 helix (dpeaa)DE-He213 Kılıçoğlu, Şeyda aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 25(2015), 4 vom: 14. Feb., Seite 977-988 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:25 year:2015 number:4 day:14 month:02 pages:977-988 https://dx.doi.org/10.1007/s00006-015-0535-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 14 02 977-988 |
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Şenyurt, Süleyman |
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Şenyurt, Süleyman misc Darboux vector misc involute curve misc ruled surface misc helix On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 |
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On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 Darboux vector (dpeaa)DE-He213 involute curve (dpeaa)DE-He213 ruled surface (dpeaa)DE-He213 helix (dpeaa)DE-He213 |
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on the differential geometric elements of the involute %${\tilde{\rm d}}%$-scroll in e3 |
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On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 |
| abstract |
Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. © Springer Basel 2015 |
| abstractGer |
Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. © Springer Basel 2015 |
| abstract_unstemmed |
Abstract Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], %${\tilde{D}}%$-scroll, which is known as the rectifying developable surface, of any curve %${\alpha}%$ and the involute%${\tilde{D}}%$-scroll of the curve %${\alpha}%$ are already defined, %${\mathbb{E}^{3}}%$. In this paper, we consider these special ruled surfaces %${\tilde{D}}%$-scroll and involute%${\tilde{D}}%$-scroll, associated to a space curve %${\alpha}%$ with curvature %${k_{1} \neq 0}%$ and involute %${\beta}%$. We will examine the differential geometric elements (such as , Weingarten map S, curvatures K and H) of the involute%${\tilde{D}}%$-scroll and %${\tilde{D}}%$-scroll relative to each other. Further we will examined the fundamental forms too. © Springer Basel 2015 |
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On the Differential Geometric Elements of the Involute %${\tilde{\rm D}}%$-Scroll in E3 |
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https://dx.doi.org/10.1007/s00006-015-0535-z |
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10.1007/s00006-015-0535-z |
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2024-07-03T13:53:44.321Z |
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