ﻻ يوجد ملخص باللغة العربية
The goal of this article is to investigate nontrivial $m$-quasi-Einstein manifolds globally conformal to an $n$-dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under the action of an $(n-1)$-dimensional translation group, we provide a complete classification when $lambda=0$ and $mgeq 1$ or $m=2-n.$
The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady quasi-Einstein manifold $(M^{n},,g)$ with positive Ricci curvature such that its potential function
In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for submanifolds of codimension two since in this case our assumptions are only of intrinsic nature.
We consider, in the Euclidean setting, a conformal Yamabe-type equation related to a potential generalization of the classical constant scalar curvature problem and which naturally arises in the study of Ricci solitons structures. We prove existence
We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.
In this paper, we prove that a compact quasi-Einstein manifold $(M^n,,g,,u)$ of dimension $ngeq 4$ with boundary $partial M,$ nonnegative sectional curvature and zero radial Weyl tensor is either isometric, up to scaling, to the standard hemisphere $