On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity

Uday Chand De; Avik De

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 4, page 1055-1072
  • ISSN: 0011-4642

Abstract

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The object of the present paper is to study almost pseudo-conformally symmetric Ricci-recurrent manifolds. The existence of almost pseudo-conformally symmetric Ricci-recurrent manifolds has been proved by an explicit example. Some geometric properties have been studied. Among others we prove that in such a manifold the vector field ρ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field ρ are geodesic. We also study some global properties of such a manifold. Finally, we study almost pseudo-conformally symmetric Ricci-recurrent spacetime. We obtain the Segre’ characteristic of such a spacetime.

How to cite

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Chand De, Uday, and De, Avik. "On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity." Czechoslovak Mathematical Journal 62.4 (2012): 1055-1072. <http://eudml.org/doc/247187>.

@article{ChandDe2012,
abstract = {The object of the present paper is to study almost pseudo-conformally symmetric Ricci-recurrent manifolds. The existence of almost pseudo-conformally symmetric Ricci-recurrent manifolds has been proved by an explicit example. Some geometric properties have been studied. Among others we prove that in such a manifold the vector field $\rho $ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field $\rho $ are geodesic. We also study some global properties of such a manifold. Finally, we study almost pseudo-conformally symmetric Ricci-recurrent spacetime. We obtain the Segre’ characteristic of such a spacetime.},
author = {Chand De, Uday, De, Avik},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre' characteristic; pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre characteristic},
language = {eng},
number = {4},
pages = {1055-1072},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity},
url = {http://eudml.org/doc/247187},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Chand De, Uday
AU - De, Avik
TI - On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 1055
EP - 1072
AB - The object of the present paper is to study almost pseudo-conformally symmetric Ricci-recurrent manifolds. The existence of almost pseudo-conformally symmetric Ricci-recurrent manifolds has been proved by an explicit example. Some geometric properties have been studied. Among others we prove that in such a manifold the vector field $\rho $ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field $\rho $ are geodesic. We also study some global properties of such a manifold. Finally, we study almost pseudo-conformally symmetric Ricci-recurrent spacetime. We obtain the Segre’ characteristic of such a spacetime.
LA - eng
KW - pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre' characteristic; pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre characteristic
UR - http://eudml.org/doc/247187
ER -

References

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