| Texto completo | |
| Autor(es): |
Zuhlke, Pedro
Número total de Autores: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | Geometriae Dedicata; v. 205, n. 1, p. 95-112, APR 2020. |
| Citações Web of Science: | 0 |
| Resumo | |
Let Mn+1 (n = 2) be a simply-connected space form of sectional curvature -.2 for some. = 0, and I an interval not containing {[}-.,.] in its interior. It is known that the domain of a closed immersed hypersurface of M whose principal curvatures lie in I must be diffeomorphic to the n-sphere Sn. These hypersurfaces are thus topologically rigid. The purpose of this paper is to show that they are also homotopically rigid. More precisely, for fixed I, the space F of all such hypersurfaces is either empty or weakly homotopy equivalent to the group of orientation-preserving diffeomorphisms of Sn. An equivalence assigns to each element of F a suitable modification of its Gauss map. For M not simply-connected, F is the quotient of the corresponding space of hypersurfaces of the universal cover of M by a natural free proper action of the fundamental group of M. (AU) | |
| Processo FAPESP: | 14/22556-3 - Geometria de subvariedades isoparamétricas do espaço de Hilbert e topologia de espaços de curvas com curvatura limitada em superfícies. |
| Beneficiário: | Pedro Paiva Zühlke d'Oliveira |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |