Identidades geométricas e resultados de rigidez em variedades do tipo estática

Abstract

In this thesis, we obtain some results of rigidity in manifolds which satises an equation of static type, for example, the static manifolds, the Ricci Solitons, the generalized Solitons, the V-static manifolds and the Einstein manifolds with a S1-static action. The methods used in ours various results are based in the analysis of integral identities in Riemannian geometry, such as Pohozaev-Schöen Identity and Reilly Identity, and in the variational techniques inspired by the Geometric Analysis.