A Note on Quasi-Yamabe Solitons on Para-Sasakian Manifolds

ABSTRACT

The object of the present paper is to prove that a para-Sasakian manifold does not admit a proper quasi-Yamabe soliton (M, g, ? , ?, µ ) and if a para-Sasakian manifold admits a quasi-Yamabe soliton (M, g, ?, ?, ?) whose soliton field is pointwise collinear with the Reeb vector field, then the quasi-Yamabe soliton reduces to Yamabe soliton whose soliton field is the V-Ric vector field, then the Ricci operator Q and the (1, 1) tensor ? commute with each other. Finally, an example is constructed to prove the non-existence of proper quasi-Yamabe solitons on para-Sasakian manifolds.

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