相关论文: On mixed super quasi-Einstein manifolds with Ricci…

In the present paper we discuss about a set of geometric properties and physical applications of a mixed quasi-Einstein spacetime$[M(QE)_{4}]$, which is a special type of nearly quasi-Einstein spacetime$[N(QE)_{4}]$. Firstly we consider a…

As a generalization of Einstein manifolds, the nearly quasi-Einstein manifolds and pseudo quasi-Einstein manifolds are both interesting and useful in studying the general relativity. In this paper, we study the extended quasi-Einstein…

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…

The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the…

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…

In the present paper we discuss about a set of geometric and physical properties of hyper-generalised quasi-Einstein spacetime. At the beginning we discuss about pseudosymmetry over a hyper-generalised quasi-Einstein spacetime. Here we…

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…

Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here we consider a…

In this work, a detailed examination of a specific case of a generalized quasi-Einstein manifold (GQE)n is provided. It begins by exploring generalized quasi-Einstein spacetimes under certain conditions. The analysis then focuses on cases…

Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…

Let (M,g) be a 2-quasi-Einstein non-conformally flat semi-Riemannian manifold of dimension > 3. We prove that if its Riemann-Christoffel curvature tensor R is a linear combination of some Kulkarni-Nomizu tensors formed by the metric tensor…

Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case,…

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…

In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\varrg$, unifying various particular cases recently studied in the literature, such as gradient Ricci solitons, Yamabe solitons and quasi-Einstein…

Conformally quasi-recurrent (CQR)_n pseudo-Riemannian manifolds are investigated, and several new results are obtained. It is shown that the Ricci tensor and the gradient of the fundamental vector are Weyl compatible tensors (the notion was…

In the present paper we introduce a semi-quasi-Einstein manifold from a semi symmetric metric connection. Among others, the popular Schwarzschild and Kottler spacetimes are shown to possess this structure. Certain curvature conditions are…

Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that…

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 call a metric quasi-Einstein if the $m$-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the…