Ruled hypersurfaces and homogeneous submanifolds in semi-Riemannian manifolds

The notion of symmetry can be defined in a rigorous way in terms of group theory. In the setting of semi-Riemannian geometry, the natural group to consider is the isometry group. In this thesis we study some specific types of submanifolds of semi-Riemannian manifolds from the viewpoint of their symm...

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Detalles Bibliográficos
Autor: Pérez Barral, Olga
Tipo de recurso: tesis doctoral
Fecha de publicación:2020
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:10347/24555
Acceso en línea:http://hdl.handle.net/10347/24555
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
Materias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Lie
Descripción
Sumario:The notion of symmetry can be defined in a rigorous way in terms of group theory. In the setting of semi-Riemannian geometry, the natural group to consider is the isometry group. In this thesis we study some specific types of submanifolds of semi-Riemannian manifolds from the viewpoint of their symmetries. On the one hand, we focus on the simplest example of Lorentzian manifold, the Minkowski spacetime, where we investigate cohomogeneity one actions. On the other hand, we turn our attention to nonflat complex space forms, where we investigate ruled hypersurfaces satisfying some additional geometric properties and we also derive a classification of homogeneous CR submanifolds.