Characterization of a paraSasakian manifold admitting Bach tensor

Year 2023, Volume: 72 Issue: 3, 826 - 838, 30.09.2023

U.c. De , Gopal Ghosh , Krishnendu De

https://doi.org/10.31801/cfsuasmas.1172289

Abstract

In the present article, our aim is to characterize Bach flat paraSasakian manifolds. It is established that a Bach flat paraSasakian manifold of dimension greater than three is of constant scalar curvature. Next, we prove that if the metric of a Bach flat paraSasakian manifold is a Yamabe soliton, then the soliton field becomes a Killing vector field. Finally, it is shown that a 3-dimensional Bach flat paraSasakian manifold is locally isometric to the hyperbolic space $H^{2n+1}(1)$.

Keywords

Bach tensor, cotton tensor, paraSasakian manifold

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