RT Dissertation/Thesis
T1 Homogeneous hypersurfaces and totally geodesic submanifolds
A1 Rodríguez Vázquez, Alberto
K1 cohomogeneity one
K1 isoparametric
K1 constant principal curvatures
K1 totally geodesic
K1 rank one
K1 symmetric spaces
K1 homogeneous spaces
K1 Kähler angle
AB This Ph.D. thesis deals with the study of certain classes of submanifolds inthe presence of symmetry.Namely, results have been derived regarding the theory of submanifolds in Riemannian homogeneous spaces witha special emphasis on symmetric spaces. In this dissertation, we will focus on two of the most natural classes ofsubmanifolds that one can study in Riemannian manifolds. These are homogeneous hypersurfaces and totallygeodesic submanifolds.Regarding the first ones, we will conclude the classification of homogeneous hypersurfaces in symmetric spaces ofrank one, by finishing the classification in quaternionic hyperbolic spaces. As for totally geodesic submanifolds, wewill derive different classifications. In particular, we will classify totally geodesic submanifolds in the followingspaces: in products of symmetric spaces of rank one, in exceptional symmetric spaces, and in Hopf-Bergerspheres.
YR 2022
FD 2022
LK http://hdl.handle.net/10347/29353
UL http://hdl.handle.net/10347/29353
LA eng
DS Minerva
RD 24 abr 2026