Hipersuperfícies mínimas compactas com índice um no espaço projetivo real

Abstract

In this dissertation, we will state and prove the Do Carmo - Ritoré - Ros theorem, which establishes that the only two-sided compact minimal hypersurfaces with index one in the real projective space RPn+1 are the totally geodesic spheres and the Clifford minimal hypersurfaces. Moreover, the only embedded ones are the Clifford hypersurfaces. A consequence is that the only two-sided compact minimal hypersurfaces that are volume preserving stable in the real projective space RPn+1 are the totally geodesic spheres and the Clifford minimal hypersurfaces.