Results 51 to 60 of about 90 (87)

Classification of curvature collineations of plane symmetric static spacetimes

Journal of Mathematical Physics, 2000
A complete classification of curvature collineations of static plane symmetric spacetimes is obtained and then a comparison between isometries and Ricci Collineations of the corresponding metrics is given.
Bokhari, Ashfaque H., Kashif, Abdul R., Qadir, Asghar   +2 more
openaire   +2 more sources

Proper curvature collineations in cylindrically symmetric static space-time

Il Nuovo Cimento B, 2004
An approach is adopted to study proper curvature collineations in Spherically symmetric static space-times by using the rank of the 6x6 Rieman matrix. It is shown that when the above space-times admit proper curvature collineations, they form an infinite dimensional vector space.
Shabbir, G., Bokhari, A.H., Kashif, A.R.
openaire   +1 more source

The Riemann tensor, the metric tensor, and curvature collineations in general relativity

Journal of Mathematical Physics, 1982
The equation xμνRμ λαβ+xμλRμ ναβ = 0, where xμν and Rμ ναβ are the components of an arbitrary symmetric tensor and of the Riemann tensor formed from the metric tensor gμν, is trivially satisfied by xμν = φgμν. Nontrivial solutions are important in various areas of general relativity such as in the study of curvature collineations, and also in the study
McIntosh, C. B. G., Halford, W. D.
openaire   +1 more source

Groups of Curvature Collineations in Riemannian Space-Times Which Admit Fields of Parallel Vectors

Journal of Mathematical Physics, 1970
By definition, a Riemannian space Vn admits a symmetry called a curvature collineation (CC) if the Lie derivative with respect to some vector ξi of the Riemann curvature tensor vanishes. It is shown that if a Vn admits a parallel vector field, then it will admit groups of CC's.
Katzin, Gerald H., Levine, Jack, Davis, William R.   +2 more
openaire   +2 more sources

Projective curvature collineation in symmetric Finsler space

2012
In this paper we study different properties of projective curvature collineations in asymmetric Finsler spaces. Several results are obtained.
PANDE, H.D., KUMAR, A., DUBEY, V.J.
openaire   +2 more sources

Proper curvature collineations in Bianchi type I space-times

Il Nuovo Cimento B, 2006
The author studies Bianchi type I space-times according to their proper curvature collineations (CCs). These curvature collineations are vector fields along which the Lie derivative of the Riemann tensor is zero. An approach is adopted connected with using the rank of the \(6\times6\) Riemann matrix, direct integration techniques, and also the theorem ...
openaire   +2 more sources

A note on proper curvature collineations in Bianchi type VIII and IX space-times

Gravitation and Cosmology, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shabbir, Ghulam, Ali, Amjad, Ramzan, M.
openaire   +2 more sources

Bianchi types of a three-parameter group of curvature collineations

General Relativity and Gravitation, 1986
The Bianchi types of the three-parameter group of curvature collineations admitted by a previously discussed family of typeN Robinson-Trautman empty space-times are obtained.
openaire   +1 more source

Curvature collineations of non-expanding and twist-free vacuum type-N metrics in general relativity

Journal of Physics A: Mathematical and General, 1980
The curvature collineation equations have been solved for the two families of Petrov type-N plane-fronted gravitational wave solutions of Einstein's vacuum field equations in general relativity. Both of these solutions always have non-trivial curvature collineations, i.e.
W D Halford, C B G McIntosh, E H Van Leeuwen   +2 more
openaire   +1 more source

Curvature Collineations: A Fundamental Symmetry Property of the Space-Times of General Relativity Defined by the Vanishing Lie Derivative of the Riemann Curvature Tensor

Journal of Mathematical Physics, 1969
A Riemannian space Vn is said to admit a particular symmetry which we call a ``curvature collineation'' (CC) if there exists a vector ξi for which £ξRjkmi=0, where Rjkmi is the Riemann curvature tensor and £ξ denotes the Lie derivative. The investigation of this symmetry property of space-time is strongly motivated by the all-important role of the ...
Katzin, Gerald H., Levine, Jack, Davis, William R.   +2 more
openaire   +2 more sources