Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Autor "Batista, Elismar Dias"
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Item Gradiente ricci solitons e variedades de Einstein com métrica produto torcido(Universidade Federal de Goiás, 2016-03-31) Batista, Elismar Dias; Souza, Marcelo Almeida de; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4797616Y0; Pina, Romildo da Silva; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782462D0; Pina, Romildo da Silva; Souza, Marcelo Almeida dea; Santos, João Paulo dosThis 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.