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On Weakly Cyclic Z Symmetric Spacetimes

Acta Mathematica Hungarica, 2016
In the reviewed paper the authors study weakly cyclic \(Z\)-symmetric spacetimes. Let \((M^n,g)\) be a Riemannian or semi-Riemannian manifold. A tensor \(Z\) given by \(Z(X,Y)=S(X,Y)+\phi g(X,Y)\), where \(S\) is the Ricci tensor and \(\phi\) is a function, is called a generalized \(Z\)-tensor.
Luca Guido Molinari, Uday Chand De
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Geodesics in Weakly Symmetric Spaces

Annals of Global Analysis and Geometry, 1997
A Riemannian manifold \(M\) is said to be weakly symmetric if for every two points \(p\) and \(q\) in \(M\) there is an isometry of \(M\) interchanging \(p\) and \(q\). The authors prove that every geodesic in a weakly symmetric space is an orbit of a one-parameter group of isometries of \(M\).
Oldrich Kowalski, Jürgen Berndt, Lieven Vanhecke   +2 more
exaly   +3 more sources

A Note on Weakly Symmetric Rings

Canadian Mathematical Bulletin, 1974
T. Nakayama showed in [2, Theorem 13] that symmetric algebras have the property that the left and right annihilators of their two-sided ideals are equal. He also gave examples [2, p. 630] to show that QF algebras with this property are not necessarily symmetric, and that weakly symmetric algebras need not have this property.
P. J. Horn
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On weakly cyclic Z symmetric manifolds

Acta Mathematica Hungarica, 2014
A Riemannian manifold \((M^n, g)\), \(n > 2\), is called ``weakly cyclic \(Z\) symmetric'' manifold if its non-zero Ricci tensor \(S\) satisfies \[ (\nabla_X S)(U, V) = A(X) S(U, V) + B(U)S(V, X) - D(V) S(X, U), \] where \(A\), \(B\), and \(D\) are \(1\)-forms, \(\nabla\) is the Levi-Civita connection on \(M\) and there exists a non-zero symmetric \((0,
U. C. De, C. A. Mantica, Y. J. Suh
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On Weakly Symmetric Spacetime

Lobachevskii Journal of Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Uday Chand De
exaly   +3 more sources

On weakly projective symmetric manifolds

, 2009
Summary: The object of the present paper is to study weakly projective symmetric manifolds and its decomposability with several non-trivial examples. Among others it is shown that in a decomposable weakly projective symmetric manifold both the decompositions are weakly Ricci symmetric.
Shaikh, A. A., Hui, Shyamal Kumar
core   +3 more sources

The Existence of Weakly Symmetric and Weakly Ricci-Symmetric Sasakian Manifolds Admitting a Quarter-Symmetric Metric Connection

Acta Mathematica Hungarica, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jai Prakash Jaiswal
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Weakly Ricci symmetric spacetimes

International Journal of Geometric Methods in Modern Physics, 2017
The objective of the present paper is to study weakly Ricci symmetric spacetimes. Among others, we prove that a weakly Ricci symmetric spacetime obeying Einstein’s field equation without cosmological constant represents stiff matter. Moreover, it is shown that the local cosmological structure of a weakly Ricci symmetric perfect fluid spacetime can be ...
De, Avik, Majhi, Pradip
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