Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
Symmetry lies at the very core of science. Indeed, geometry was defined by Felix Klein as the study of those properties in a space that are invariant under a given transformation symmetry group. In this thesis, we study certain kind of geometrical objects from the viewpoint of their symmetries in th...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/19772 |
| Acceso en línea: | http://hdl.handle.net/10347/19772 |
| Access Level: | acceso abierto |
| Palabra clave: | Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial Materias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de Riemann |
| Sumario: | Symmetry lies at the very core of science. Indeed, geometry was defined by Felix Klein as the study of those properties in a space that are invariant under a given transformation symmetry group. In this thesis, we study certain kind of geometrical objects from the viewpoint of their symmetries in the context of symmetric spaces of non-compact type. More precisely, we have classified isoparametric hypersurfaces in complex hyperbolic spaces and spacelike isoparametric hypersurfaces in anti-De Sitter spaces, produced a large family of non-totally geodesic CPC submanifolds (submanifolds whose principal curvatures do not depend on the normal directions) that are not orbits of cohomogeneity one actions and classified certain austere orbits arising from the theory of parabolic subgroups. |
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