Homogeneous hypersurfaces in symmetric spaces

Resumo

In this thesis, we tackle the classification problem for homogeneous hypersurfaces in symmetric spaces. The results can be divided into two lines. The first of these consists in the development of a structural result for cohomogeneity one actions on symmetric spaces of noncompact type. This result guarantees that any such action can be constructed by one of five standard methods, easily described in terms of Lie algebras. The second line investigates cohomogeneity one actions on products of symmetric spaces of different types. Under certain hypotheses, one can reduce the study of these actions to each factor. This allowed us to produce a classification of codimension one homogeneous foliations on simply connected symmetric spaces.