Conformal Ricci Soliton in Lorentzian α -Sasakian Manifolds

Tamalika Dutta; Nirabhra Basu; Arindam BHATTACHARYYA

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 2, page 57-70
  • ISSN: 0231-9721

Abstract

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In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian α -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian α -Sasakian manifold admitting conformal Ricci soliton is η -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian α -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian α -Sasakian manifold M with projective curvature tensor admitting conformal Ricci soliton is η -Einstein manifold. We have also established an example of 3-dimensional Lorentzian α -Sasakian manifold.

How to cite

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Dutta, Tamalika, Basu, Nirabhra, and BHATTACHARYYA, Arindam. "Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.2 (2016): 57-70. <http://eudml.org/doc/287916>.

@article{Dutta2016,
abstract = {In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $\alpha $-Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian $\alpha $-Sasakian manifold $M$ with projective curvature tensor admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also established an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold.},
author = {Dutta, Tamalika, Basu, Nirabhra, BHATTACHARYYA, Arindam},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor},
language = {eng},
number = {2},
pages = {57-70},
publisher = {Palacký University Olomouc},
title = {Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds},
url = {http://eudml.org/doc/287916},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Dutta, Tamalika
AU - Basu, Nirabhra
AU - BHATTACHARYYA, Arindam
TI - Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 2
SP - 57
EP - 70
AB - In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $\alpha $-Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian $\alpha $-Sasakian manifold $M$ with projective curvature tensor admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also established an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold.
LA - eng
KW - Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor
UR - http://eudml.org/doc/287916
ER -

References

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