Sobre variedades m-quase-Einstein: rigidez e rórmulas estruturais

Abstract

In this dissertation, we treat about m-quasi-Einstein manifolds and one of its generalizations. We present demonstrations of rigidity results and structural formulasobtained by several authors in distinct publications, standing out the characterizationof complete m-quasi-Einstein Riemannian manifolds as space forms, given by Barros and Ribeiro at a work published in 2014, whose same thesis was obtained from other hypothesis provided by Barros and Gomes at a 2013 publication. We also show topo- logical results about volume growthof geodesic balls on quasi-Einstein manifolds that are also Einsten, presented by Barros, Ribeiro and Batista in 2014. Also noteworthy the approach of the work due to Catino at the paper Generalized quasi-Einstein manifolds with harmonic Weyl tensor, published in 2012 on the Mathematische Zeitschrift, where show up that a complete Einstein manifold with quasi-Einstein structure, harmonic Weyl tensor and zero radial Weyl curvature is locally a warped product with (n − 1)-dimensional Einstein ber.