Quasi-Einstein manifolds with structure of warped product

被引：1
|
作者：
Correia, Paula [1 ]
Pina, Romildo [1 ]
机构：
[1] Univ Fed Goias, IME, Caixa Postal 131, BR-74001970 Goiania, Go, Brazil
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2020年 / 72卷
关键词：
Semi-Riemannian metric; Quasi-Einstein manifold; Einstein manifold; Warped product;
D O I：
10.1016/j.difgeo.2020.101658
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we prove that, under certain conditions, in a quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all the quasi-Einstein manifolds when r-Bakry-Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n - 1)-dimensional translation group and the fiber is Ricci-flat. As an application, we have built a family of Ricci-flat Einstein warped product whose base is not locally conformally flat. (C) 2020 Elsevier B.V. All rights reserved.
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页数：16
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