Ruled hypersurfaces and homogeneous submanifolds in semi-Riemannian manifolds

• Autores: Olga Pérez Barral
• Directores de la Tesis: José Carlos Díaz-Ramos (dir. tes.), Miguel Domínguez-Vázquez (dir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2020
• Idioma: inglés
• Tribunal Calificador de la Tesis: Luis Hernández Lamoneda (presid.), José Antonio Oubiña Galiñanes (secret.), Alma Luisa Albujer Brotons (voc.)
• Materias:
  • Matemáticas
    • Álgebra
      • Álgebra de Lie
    • Geometría
      • Geometría diferencial
      • Geometría de Riemann
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • 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.