Related papers: On Quasi-Einstein Sequential Warped Product Manifo…
The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we…
Necessary and sufficient conditions for a Riemannian product to be conformally equivalent to an Einstein manifold are given. Such spaces which are complete are characterized.
We study Einstein warped space with a quarter symmetric connection. As a result, first, we find basic results on curvature, Ricci and scalar tensors with respect to the quarter symmetric connection. Moreover, we prove some results…
In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension $n\geq 3$ is locally a warped product with $(n-1)$-dimensional fibers of constant curvature. This result includes also the case of…
Einstein like $(\varepsilon)$-para Sasakian manifolds are introduced. For an $(\varepsilon) $-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar…
In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold…
The aim of this paper is to extend the notion of all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed generalized quasi-Einstein manifold, pseudo generalized quasi-Einstein manifold and many more and name it…
We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a…
In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) $T$-flat quasi-Einstein manifolds with constant scalar curvature, where the…
We introduce sequential warped product submanifolds of Kaehler manifolds, provide examples and establish Chen's inequality for such submanifolds. The equality case is also studied. Moreover, by inspiring Lawson and Simons's integral…
We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where…
In this paper, we define the semi-symmetric metric connection on super Riemannian manifolds. We compute the semi-symmetric metric connection and its curvature tensor and its Ricci tensor on super warped product spaces. We introduce two kind…
The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the…
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…
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.
We extend the estimate obtained in [1] for the mean curvature of a cylindrically bounded proper submanifold in a product manifold with an Euclidean space as one factor to a general product ambient space endowed with a warped product…
We study hypersurfaces in the pseudo-Euclidean space $\mathbb{E}^{n+1}_s$, which write as a warped product of a $1$-dimensional base with an $(n-1)$-manifold of constant sectional curvature. We show that either they have constant sectional…
In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for…
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the…
Recently, it is proven that generalized Robertson-Walker space-times in all orthogonal subspaces of Gray's decomposition but one(unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by…