A family of warped product semi-Riemannian Einstein metrics

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• 作者：Má ; rcio Lemes de Sousa^a ; ^{marciolemesew@yahoo.com.br} ; Romildo Pina^b ; ¹ ; ^{romildo@ufg.br}
• 关键词：53C21 ; 53C50 ; 53C25
• 刊名：Differential Geometry and its Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：50
• 期：Complete
• 页码：105-115
• 全文大小：319 K
• 卷排序：50

文摘

We study warped product semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n  -dimensional pseudo-Euclidean space and invariant under the action of an (n−1)(n−1)-dimensional translation group. We provide all such solutions in the case Ricci-flat when the base is conformal to an n  -dimensional pseudo-Euclidean space, invariant under the action of an (n−1)(n−1)-dimensional translation group and the fiber F is Ricci-flat. In particular, we obtain explicit solutions, in the case vacuum, for the Einstein field equation.