Ribaucour transformations and their singularities
Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of R...
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Gespeichert in:
| Autor*in: |
Ogata, Yuta [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of geometry - Springer International Publishing, 1971, 113(2021), 1 vom: 30. Nov. |
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| Übergeordnetes Werk: |
volume:113 ; year:2021 ; number:1 ; day:30 ; month:11 |
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| DOI / URN: |
10.1007/s00022-021-00618-y |
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OLC2077553790 |
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| 520 | |a Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities. | ||
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| 650 | 4 | |a singularity theory | |
| 650 | 4 | |a transformation theory | |
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10.1007/s00022-021-00618-y doi (DE-627)OLC2077553790 (DE-He213)s00022-021-00618-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ogata, Yuta verfasserin (orcid)0000-0002-2832-0095 aut Ribaucour transformations and their singularities 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities. Surface theory singularity theory transformation theory Enthalten in Journal of geometry Springer International Publishing, 1971 113(2021), 1 vom: 30. Nov. (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:113 year:2021 number:1 day:30 month:11 https://doi.org/10.1007/s00022-021-00618-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_4277 AR 113 2021 1 30 11 |
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10.1007/s00022-021-00618-y doi (DE-627)OLC2077553790 (DE-He213)s00022-021-00618-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ogata, Yuta verfasserin (orcid)0000-0002-2832-0095 aut Ribaucour transformations and their singularities 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities. Surface theory singularity theory transformation theory Enthalten in Journal of geometry Springer International Publishing, 1971 113(2021), 1 vom: 30. Nov. (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:113 year:2021 number:1 day:30 month:11 https://doi.org/10.1007/s00022-021-00618-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_4277 AR 113 2021 1 30 11 |
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Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract The Ribaucour transformation is a generalization of parallel surfaces and Darboux transformations. It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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It has been studied by many researchers. In this paper, first we introduce the construction of Ribaucour transforms via Cauchy–Kovalevskaya theorem, including an explicit integral formula of Ribaucour transformations for surfaces of revolution. In the latter half of this paper, we also study the singularities appearing on Ribaucour transforms and give the criteria for cuspidal edges, swallowtails, cuspidal cross caps, $$D_4^{\pm }$$-singularities.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Surface theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">singularity theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">transformation theory</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of geometry</subfield><subfield code="d">Springer International Publishing, 1971</subfield><subfield code="g">113(2021), 1 vom: 30. Nov.</subfield><subfield code="w">(DE-627)129288993</subfield><subfield code="w">(DE-600)120140-2</subfield><subfield code="w">(DE-576)014470527</subfield><subfield code="x">0047-2468</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:113</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:1</subfield><subfield code="g">day:30</subfield><subfield code="g">month:11</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00022-021-00618-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_30</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">113</subfield><subfield code="j">2021</subfield><subfield code="e">1</subfield><subfield code="b">30</subfield><subfield code="c">11</subfield></datafield></record></collection>
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