Geodesic
Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 57-70 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53C25, 53C44, 53D10
Keywords: Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor 
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Dutta, Tamalika; Basu, Nirabhra; BHATTACHARYYA, Arindam. Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 57-70. http://geodesic.mathdoc.fr/item/AUPO_2016_55_2_a5/