Gradiente ricci solitons e variedades de Einstein com métrica produto torcido

This work is based on the articles [26] and [27], where we studied Einstein manifolds and gradient Ricci soliton with twisted product structure. As a result, we prove the following: if M is an Einstein warped product space with nonpositive scalar curvature and compact base, then M is a Riemannian pr...

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Detalles Bibliográficos
Autor: Batista, Elismar Dias
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2016
País:Brasil
Institución:Universidade Federal de Goiás (UFG)
Repositorio:Repositório Institucional da UFG
Idioma:portugués
OAI Identifier:oai:repositorio.bc.ufg.br:tede/5693
Acceso en línea:http://repositorio.bc.ufg.br/tede/handle/tede/5693
Access Level:acceso abierto
Palabra clave:Produto torcido
Variedade de Einstein
Gradiente ricci soliton
Warped product
Einstein manifolds
Gradient ricci solitons
ALGEBRA::GEOMETRIA ALGEBRICA
Descripción
Sumario:This work is based on the articles [26] and [27], where we studied Einstein manifolds and gradient Ricci soliton with twisted product structure. As a result, we prove the following: if M is an Einstein warped product space with nonpositive scalar curvature and compact base, then M is a Riemannian product space. Besides, we show that the Riemannian product Rp×F is a gradient Ricci soliton if and only if F is Ricci soliton gradient. Then, we show that the warped product R×f B is gradient Ricci solitons with f ′′ 6= 0, therefore F is Einstein. By using these results, we build nontrivial examples of gradient Ricci soliton where the fiber is either an Einstein manifold or a nontrivial gradient Ricci soliton.