Conformal Ricci Soliton in an Indefinite Trans-Sasakian Manifold

Girish Babu, S. , Reddy, P. S. K. , Somashekhara, G.
Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 3.

Abstract:
Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. A new class of \(n\)-dimensional almost contact manifold namely trans-Sasakian manifold was introduced by Oubina in 1985 and further study about the local structures of trans-Sasakian manifolds was carried by several authors. As a natural generalization of both Sasakian and Kenmotsu manifolds, the notion of trans-Sasakian manifolds, which are closely related to the locally conformal Kahler manifolds introduced by Oubina. This paper deals with the study of conformal Ricci solitons within the framework of indefinite trans-Sasakian manifold. Further, we investigate the certain curvature tensor on indefinite trans-Sasakian manifold. Also, we have proved some important results.

Keywords: indefinite trans-Sasakian manifold, trans-Sasakian manifold, Ricci flow, conformal Ricci flow

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