The aim of this paper is to study complete (noncompact) m-quasi-Einstein manifolds with λ=0 satisfying a fourth-order vanishing condition on the Weyl tensor and zero radial Weyl curvature. In this case, we are able to prove that an m-quasi-Einstein manifold (m>1) with λ=0 on a simply connected n-dimensional manifold(M n , g), (n ≥ 4), of nonnegative Ricci curvature and zero radial Weyl curvature must be a warped product with (n–1)–dimensional Einstein fiber, provided that M has fourth-order divergence-free Weyl tensor (i.e. div4W =0).

中文翻译：

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关于 Weyl 张量上具有消失状态的非紧致准爱因斯坦流形分类的注释

本文的目的是研究完整的（非紧凑的）米-准爱因斯坦流形，λ=0，满足外尔张量的四阶消失条件和​​零径向外尔曲率。在这种情况下，我们可以证明一个米-准爱因斯坦流形（米>1) 在简单连接上 λ=0n-维流形（米 n ,G), (n≥ 4)，非负 Ricci 曲率和零径向 Weyl 曲率必须是具有 (n–1)–维爱因斯坦纤维，前提是米具有四阶无散外尔张量（即 div4W=0)。