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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| 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 |
| 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. |
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