Um estudo sobre a utilização da mudança conforme da métrica riemanniana em variedades completas.

Abstract

In the present work, an important tool in the area of Riemannian Geometry will be studied, the conformal change of a Riemannian metric. Making use of such a tool in the context of complete manifolds, three main theorems will be proved: a pinching theorem for complete submanifolds of the sphere, a generalization of the Bonnet-Myers theorem and a diameter estimate for a stable H-hypersurface immersed in an ambient manifold with sectional curvature bounded from below.