Almost conformal Ricci solituons on $3$-dimensional trans-Sasakian manifold

Authors : Tamalika DUTTA, Nirabhra BASU, Arindam BHATTACHARYYA

Pages : 1379-1392

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Publication Date : 2016-10-01

Article Type : Research Paper

Abstract :In this paper we have shown that if a $3$-dimensional trans-Sasakian manifold M admits conformal Ricci soliton $insert ignore into journalissuearticles values(g,V,\lambda );$ and if the vector field $V$ is point wise collinear with the unit vector field $\xi$, then $V$ is a constant multiple of $\xi$. Similarly we have proved that under the same condition an almost conformal Ricci soliton becomes conformal Ricci soliton. We have also shown that if a $3$-dimensional trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton, then the manifold is an Einstein manifold.
Keywords : conformal Ricci soliton, almost conformal Ricci soliton, conformal gradient shrinking Ricci soliton, trans Sasakian manifold