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Quasi-Einstein manifolds with structure of warped product
Differential Geometry and its Applications ( IF 0.6 ) Pub Date : 2020-06-17 , DOI: 10.1016/j.difgeo.2020.101658 Paula Correia , Romildo Pina
中文翻译:
具有变形产品结构的拟爱因斯坦流形
更新日期:2020-06-17
Differential Geometry and its Applications ( IF 0.6 ) Pub Date : 2020-06-17 , DOI: 10.1016/j.difgeo.2020.101658 Paula Correia , Romildo Pina
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 -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.
中文翻译:
具有变形产品结构的拟爱因斯坦流形
在本文中,我们证明了在某些条件下,在准爱因斯坦半黎曼弯曲产品中,纤维必定是爱因斯坦流形。当r-Bakry-Emery张量为零,基数与n维拟欧几里德空间共形时,我们提供所有拟爱因斯坦流形,在维平移群,纤维是Ricci-flat。作为一种应用,我们建立了一系列Ricci-flat爱因斯坦翘曲产品,其产品的底座不是局部保形的。