Conformal hypersurfaces with the same Gauss map
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- by Marcos Dajczer and E. Vergasta PDF
- Trans. Amer. Math. Soc. 347 (1995), 2437-2456 Request permission
Abstract:
In this paper we provide a complete classification of all hypersurfaces of Euclidean space which admit conformal deformations, other than the ones obtained through conformal diffeomorphisms of the ambient space, preserving the Gauss map.References
- E. Cartan, La déformation des hypersurfaces dans l’espace conforme réel à $n \ge 5$ dimensions, Bull. Soc. Math. France 45 (1917), 57–121 (French). MR 1504762, DOI 10.24033/bsmf.975
- M. do Carmo and M. Dajczer, Rotation hypersurfaces in spaces of constant curvature, Trans. Amer. Math. Soc. 277 (1983), no. 2, 685–709. MR 694383, DOI 10.1090/S0002-9947-1983-0694383-X
- Manfredo do Carmo and Marcos Dajczer, Conformal rigidity, Amer. J. Math. 109 (1987), no. 5, 963–985. MR 910359, DOI 10.2307/2374496
- Marcos Dajczer, Submanifolds and isometric immersions, Mathematics Lecture Series, vol. 13, Publish or Perish, Inc., Houston, TX, 1990. Based on the notes prepared by Mauricio Antonucci, Gilvan Oliveira, Paulo Lima-Filho and Rui Tojeiro. MR 1075013
- Marcos Dajczer and Detlef Gromoll, Gauss parametrizations and rigidity aspects of submanifolds, J. Differential Geom. 22 (1985), no. 1, 1–12. MR 826420
- Marcos Dajczer and Detlef Gromoll, Gauss parametrizations and rigidity aspects of submanifolds, J. Differential Geom. 22 (1985), no. 1, 1–12. MR 826420
- Patrick J. Ryan, Homogeneity and some curvature conditions for hypersurfaces, Tohoku Math. J. (2) 21 (1969), 363–388. MR 253243, DOI 10.2748/tmj/1178242949
- Enaldo Silva Vergasta, Conformal immersions with the same Gauss map (conformal immersion/Gauss map), An. Acad. Brasil. Ciênc. 59 (1987), no. 3, 145–147 (1988). MR 938564
- Enaldo Silva Vergasta, Conformal deformations preserving the Gauss map, Pacific J. Math. 156 (1992), no. 2, 359–369. MR 1186811, DOI 10.2140/pjm.1992.156.359
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 2437-2456
- MSC: Primary 53C42; Secondary 53A30, 53C40
- DOI: https://doi.org/10.1090/S0002-9947-1995-1297522-3
- MathSciNet review: 1297522