Rigidez de variedades tipo-Einstein gradiente

Abstract

This dissertation is based on the detailed study of rigidity results obtained in the preprint entitled “A note on gradient Einstein-type manifolds” due to José N. V. Gomes [arXiv:1710.10549, preprint 2017]. More precisely, it has been proved that a compact gradient Einstein-type manifold with constant scalar curvature is isometric to a standard sphere with potential function explicitly given. In noncompact case, was assumed the hypotheses of Karp’s Theorem and constant scalar curvature to deduce that a gradient Einstein-type manifold is isometric to a Euclidean space, a hyperbolic space or a Einstein warped product. Finally, under certain conditions of the parameters, it has been shown that a homogeneous, noncompact and nondegenerate gradient Einstein-type manifold is Einstein.