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.

中文翻译：

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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$（ñ-\mathrm{1个}）$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。