Related papers: Comment on Ricci Collineations for spherically sym…
Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of $\xi^a(x^b)$ is different from zero and (ii) two components of $\xi^a(x^b)$ are…
The main objective of this paper is to control the geometry of null cones with time foliation in Einstein vacuum spacetime under the assumptions of small curvature flux and a weaker condition on the deformation tensor for $\bT$. We…
The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, we consider homogeneous Finsler spaces with square metric and Randers…
We prove the equivalence between the several notions of generalized Ricci curvature found in the literature. As an application, we characterize when the total generalized Ricci tensor is symmetric.
We consider three- and four-dimensional pseudo-Riemannian generalized symmetric spaces, whose invariant metrics were explicitly described in [15]. While four-dimensional pseudo-Riemannian generalized symmetric spaces of types A, C and D are…
Some known results on torsionfree connections with skew-symmetric Ricci tensor on surfaces are extended to connections with torsion, and Wong's canonical coordinate form of such connections is simplified.
We derive spherically symmetric solutions of the classical \lambda-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a 3 + 1 decomposition of the…
Conformal Ricci and conformal matter collineations for the combination of two perfect fluids in General Relativity are investigated. We study the existence of timelike and spacelike conformal Ricci and matter collineations by introducing…
In this article, we study $c$-spherical Ricci metrics, that is, Riemannian metrics whose Gaussian curvature $K$ satisfies \begin{equation*} (K - c)\Delta K - |\nabla K|^2 - 4K(K - c)^2 = 0, \end{equation*} for some $c>0$. We explicitly…
Generalized Robertson-Walker spacetimes extend the notion of Robertson-Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization in terms of a timelike concircular vector.…
Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs space- times are classified according to their Ricci collineation vector (RCV) field of the form (i)-(iv) one component of $\xi^a (x^b)$ is nonzero, (v)-(x) two…
In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static spacetimes by their matter inheritance symmetries. It is shown that when the energy-momentum tensor is degenerate,…
In this paper, we prove that any K\"ahler Ricci shrinker surface has bounded sectional curvature. Combining this estimate with earlier work by many authors, we provide a complete classification of all K\"ahler Ricci shrinker surfaces.
In this paper, we prove some rigidity theorems for shrinking gradient Ricci solitons with nonnegative sectional curvature.
The main result of the paper is a computation of the Ricci curvature of $\DS/S^1$. Unlike earlier results on the subject, we do not use the K\"{a}hler structure symmetries to compute the Ricci curvature, but rather rely on classical…
In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$, $\R{n}$ and $\R{}\times S^{n-1}$ are,…
A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated…
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 article, we characterize a Lorentzian manifold $\mathcal{M}$ with a semi-symmetric metric connection. At first, we consider a semi-symmetric metric connection whose curvature tensor vanishes and establish that if the associated…
A subclassification of stationary spacetimes, endowed with one timelike and one spacelike Killing vectors, i.e., Petrov $G{_2}I$ on $T_2$ spaces, is proposed. Special attention deserves the Collison's theorem [1] and the branch of metrics…