Submanifolds and actions on homogeneous manifolds

• Autores: Juan Manuel Lorenzo Naveiro
• Directores de la Tesis: José Carlos Díaz-Ramos (dir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2025
• Idioma: inglés
• Tribunal Calificador de la Tesis: José Miguel Figueroa O'farril (presid.) , Víctor Sanmartín López (secret.) , Alma Luisa Albujer Brotons (voc.)
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • The objective of this Ph.D. thesis is to treat several classification problems concerning submanifolds and geometric structures on homogeneous manifolds with different degrees of symmetry. There are three main research lines that we pursue in this thesis. The first one is that of polar actions on symmetric spaces, where we classify polar homogeneous foliations of codimension two on irreducible symmetric spaces of noncompact type, as well as polar homogeneous foliations on the Cayley hyperbolic plane and standard polar foliations on quaternionic hyperbolic spaces. The second line is the study of totally geodesic submanifolds; we classify totally geodesic submanifolds of the homogeneous nearly Kähler 6-manifolds and their cones with special holonomy. The last topic is that of kinematical algebras and homogeneous spacetimes, in which we classify (3,2)-kinematical Lie algebras with spatial isotropy of dimension greater than two.