Ruled hypersurfaces and homogeneous submanifolds in semi-Riemannian manifolds

  1. Olga Pérez Barral
Dirixida por:
  1. José Carlos Díaz-Ramos Director
  2. Miguel Domínguez-Vázquez Director

Universidade de defensa: Universidade de Santiago de Compostela

Ano de defensa: 2020

  1. Luis Hernández Lamoneda Presidente/a
  2. José Antonio Oubiña Galiñanes Secretario
  3. Alma Luisa Albujer Brotons Vogal
  1. Departamento de Matemáticas

Tipo: Tese


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.