Related papers: Rigidity of Quasi-Einstein Metrics

Quasi-Einstein manifolds are well-studied generalizations of Einstein manifolds. This includes gradient Ricci solitons and has a natural correspondence with the warped product Einstein manifolds. A quasi-Einstein metric is said to be rigid…

We study the modified Ricci solitons as a new class of Einstein type metrics that contains both Ricci solitons and $n$-quasi-Einstein metrics. This class is closely related to the construction of the Ricci solitons that are realised as…

We investigate K\"ahler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton…

In this paper, we study the quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection. We give the expressions of the Ricci tensors and scalar curvatures for the bases and fibres. In some…

We call a metric $m$-quasi-Einstein if $Ric_X^m$ (a modification of the $m$-Bakry-Emery Ricci tensor in terms of a suitable vector field $X$) is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which…

As part of a programme to classify quasi-Einstein metrics $(M,g,X)$ on closed manifolds and near-horizon geometries of extreme black holes, we study such spaces when the vector field $X$ is divergence-free but not identically zero. This…

The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a…

We call a metric $m$-quasi-Einstein if $Ric_X^m$, which replaces a gradient of a smooth function $f$ by a vector field $X$ in $m$-Bakry-Emery Ricci tensor, is a constant multiple of the metric tensor. It is a generalization of Einstein…

Smooth metric measure spaces have been studied from the two different perspectives of Bakry-\'Emery and Chang-Gursky-Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization…

A Riemannian metric $\wht{g}$ with Ricci curvature $\wht{\ri}$ is called nontrivial quasi-Einstein, in the sense of Case, Shu and Wei, if it satisfies $(-a/f)\wht{\nab} df+\wht{\ri}=\lambda \wht{g}$, for a smooth nonconstant function $f$…

The aim of this note is to give an explicit description of quasi-Einstein metrics on $\Bbb{H}^{n}\times \Bbb{R}.$ We shall construct two examples of quasi-Einstein metrics on this manifold and then we shall prove the uniqueness of these…

In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide…

In this article we give a classification of three dimensional m-quasi Einstein manifolds with two distinct Ricci-eigen values. Our study provides explicit description of local and complete metrics and potential functions. We also describe…

In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the $m$-Quasi Einstein…

In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be…

In this paper we characterize the Einstein metrics in such broader classes of metrics as almost $\eta$-Ricci solitons and $\eta$-Ricci solitons on Kenmotsu manifolds, and generalize some results of other authors. First, we prove that a…

Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a…

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, K\"ahler-Einstein manifolds. The quasi-Einstein metrics are related to various gradient K\"ahler-Ricci…

The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces. Quasi-Einstein metrics serve also as solution to the Ricci flow equation. Here, the Riemannian metric is replaced by a Hessian…

We show that all compact quasi-Einstein metrics of constant scalar curvature in dimension three are locally homogeneous. We accomplish this by using the equivalence of constant scalar curvature quasi-Einstein metrics $(M,g,X)$ and…