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

• Autor(a) principal: Costa, Johnatan da Silva
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/123456789/21139
• topic: Variedade quase-Einstein; Resultados de rigidez; Formas espaciais; Tensor de Weyl; Produto warped; quasi-Einstein manifolds; Rigidity results; Space forms; Weyl tensor; Warped product; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

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.