Díez Ramos, José CarlosDomínguez Vázquez, MiguelVidal Castiñeira, CristinaUniversidade de Santiago de Compostela. Facultade de Matemáticas. Departamento de Matemáticas2016-08-252016-08-252016-08-25http://hdl.handle.net/10347/14866In this PhD thesis we study submanifolds in complex projective and hyperbolic spaces. More specifically, we classify isoparametric and Terng-isoparametric submanifolds. The former correspond to principal orbits of polar actions, whereas the latter are homogeneous but not necessarily arising from polar actions. We also study real hypersurfaces with two distinct principal curvatures, show that there are non-Hopf inhomogeneous examples, and characterize them. Using the method of equivariant geometry, we investigate strongly 2-Hopf hypersurfaces and give some applications for Levi-flat and constant mean curvature hypersurfaces. Finally, we classify austere hypersurfaces such that the number of nontrivial projections of the Hopf vector field onto the principal curvature spaces is less or equal than two; all the examples are ruled in this case.engEsta obra atópase baixo unha licenza internacional Creative Commons BY-NC-ND 4.0. Calquera forma de reprodución, distribución, comunicación pública ou transformación desta obra non incluída na licenza Creative Commons BY-NC-ND 4.0 só pode ser realizada coa autorización expresa dos titulares, salvo excepción prevista pola lei. Pode acceder Vde. ao texto completo da licenza nesta ligazón: https://creativecommons.org/licenses/by-nc-nd/4.0/deed.glhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.glComplex projective and hyperbolic planesIsoparametric submanifoldsNon-Hopf real hypersurfacesPolar actionsMaterias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencialdoctoral thesisopen access