Classificação das subvariedades totalmente umbílicas de Sn x R

Abstract

In this thesis, we will present a classification for the umbilical submanifolds of arbitrary dimension and codimension of S n × R, based on the work by Bruno Mendonça and Ruy Tojeiro in [11]. The classification that will be presented extends the current classification of the umbilic surfaces in S 2 × R by Souam and Toubiana in [12] as well as the local description of the umbilical hypersurfaces S n × R by Van der Veken and Vrancken in [15] for codimensions greater than one. In both works, the umbilic surfaces and hypersurfaces are of rotation type. It will be shown here that the submanifolds studied in this work are also of rotation type and we will present explicit parametrization.