Related papers: On semi-Quasi-Einstein Manifold

An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…

Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…

This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…

In this brief survey, we will remark the interaction among the Hessian tensor on a semi-Riemannian manifold and some of the several questions in Lorentzian (and also in semi-Riemannian) geometry where this 2-covariant tensor is involved. In…

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…

In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar…

In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold,…

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…

The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the…

Advances in modern physics since Einstein have made the nonsymmetric metric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric tensor associated with electromagnetism, more…

Spinorial geometry techniques have recently been used to classify all half supersymmetric solutions in gauged five dimensional supergravity with vector multiplets. In this paper we consider solutions for which at least one of the Killing…

We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.

We introduce and study a special class of almost contact metric manifolds, which we call anti-quasi-Sasakian (aqS). Among the class of transversely K\"ahler almost contact metric manifolds $(M,\varphi, \xi,\eta,g)$, quasi-Sasakian and…

There are considered 4-dimensional pseudo-Riemannian spaces with inner products of signature (3,1) and (2,2). The objects of investigation are space-like and time-like hyperspheres in the respective cases. These hypersurfaces are equipped…

Semi-classical gravity is an approximation to quantum gravity where gravity is treated classically and matter quantum mechanically. Matter is described by quantum field theory on curved space-time, whereas gravity is described by a…

In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-$k$-curved metrics}. Quasi-$k$-curved metrics generalize the metrics of space forms. We construct explicit…

The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E…

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we…

A vector field $V$ on any (semi-)Riemannian manifold is said to be mixed Killing if for some nonzero smooth function $f$, it satisfies $L_VL_Vg=fL_Vg$, where $L_V$ is the Lie derivative along $V$. This class of vector fields, as a…