The object of the present paper is to study weakly concircular symmetric and weakly concircular Ricci symmetric Kenmotsu manifolds.

We study an even dimensional manifold with a pseudo-Riemannian metric with arbitrary signature and arbitrary dimensions. We consider the Ricci flat equations and present a procedure to construct solutions to some higher (even) dimensional Ricci flat field equations from the four dimensional Ricci flat metrics. When the four dimensional Ricci flat geometry corresponds to a colliding gravitationa...

We present a novel colon flattening algorithm using the discrete Ricci flow. The discrete Ricci flow is a powerful tool for designing Riemannian metrics on surfaces with arbitrary topologies by user-defined Gaussian curvatures. Moreover, the discrete Ricci flow deforms the Riemannian metric on the surface conformally and minimizes the global distortion, which means the local shape is well prese...

This study is concerned with some results on generalized weakly symmetric and Ricci-symmetric $\alpha$-cosymplectic manifolds. We prove the necessary sufficient conditions for an manifold to be Ricci-symmetric. On basis of these results, we give one proper example

Static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor (det.(Rα) 6= 0). It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. Some new metrics admitting proper Ricci collineations are also investigated. PACS numbers: 04.20.-q, 04.20.Jb

Introduction. In [5], J. Milnor cited "understanding the Ricci tensor Rik = J^ Rt'kl 9J as a fundamental problem of present-day mathematics. A basic issue, then, is to determine which symmetric covariant tensors of rank two can be Ricci tensors of Riemannian metrics. The definition of Ricci curvature casts the problem of finding a metric g which realizes a given Ricci curvature R as one of solv...

We derive matter collineations for some static spherically symmetric spacetimes and compare the results with Killing, Ricci and Curvature symmetries. We conclude that matter and Ricci collineations are not, in general, the same.

In this paper we study weakly symmetric and special weakly Ricci symmetric Lorentzian β-Kenmotsu manifolds and obtained some interesting results. 2000 Mathematics Subject Classification: 53C10, 53C15.

In the present study, we considered 3-dimensional generalized (κ, μ)-contact metric manifolds. We proved that a 3-dimensional generalized (κ, μ)-contact metric manifold is not locally φ-symmetric in the sense of Takahashi. However such a manifold is locally φ-symmetric provided that κ and μ are constants. Also it is shown that if a 3-dimensional generalized (κ, μ) -contact metric manifold is Ri...

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metri...