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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
(1987)
Conformal rigidity
- Publisher
- Springer Journals
- Copyright
- Copyright © 2019 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-019-00173-w
- Publisher site
- See Article on Publisher Site
Abstract
n n+1 In this paper we classify Euclidean hypersurfaces f : M → R with a principal curvature of multiplicity n − 2 that admit a genuine conformal deformation f : M → n+2 n n+2 R . That f : M → R is a genuine conformal deformation of f means that it is a conformal immersion for which there exists no open subset U ⊂ M such that the ˜ ˜ restriction f | is a composition f | = h ◦ f | of f | with a conformal immersion U U U U n+2 n+1 h : V → R of an open subset V ⊂ R containing f (U ). Keywords Genuine conformal deformations · Euclidean hypersurfaces · Envelopes of two-parameter congruences of hyperspheres Mathematics Subject Classification 53 B25 · 53 C42 · 53 A30 1 Introduction n n+1 Euclidean hypersurfaces f : M → R that are free of flat points (respectively, free of points where the multiplicity of some principal curvature is greater than or equal to n n+1 n − 1) and admit an isometric (respectively, conformal) deformation g : M → R that is not isometrically congruent (respectively, conformally congruent)
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Oct 31, 2019