Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
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Título: | Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type |
Autor/a: | Sanmartín López, Víctor |
Dirección/Titoría: | Díaz Ramos, José Carlos Domínguez Vázquez, Miguel |
Centro/Departamento: | Universidade de Santiago de Compostela. Centro Internacional de Estudos de Doutoramento e Avanzados (CIEDUS) Universidade de Santiago de Compostela. Escola de Doutoramento Internacional en Ciencias e Tecnoloxía Universidade de Santiago de Compostela. Programa de Doutoramento en Matemáticas |
Palabras chave: | Symmetric spaces of non-compact type | Isoparametric hypersurfaces | Homogeneous submanifolds | |
Data: | 2019 |
Resumo: | 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. |
URI: | http://hdl.handle.net/10347/19772 |
Dereitos: | Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
Coleccións
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- Área de Ciencias [947]
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