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- W4362508902 abstract "Abstract We consider a Riemannian manifold ( M , g ) admitting a concurrent-recurrent vector field for which the metric g is a Yamabe soliton or a τ -quasi Yamabe gradient soliton. We show that if the metric of a Riemannian three-manifold ( M , g ) admitting a concurrent-recurrent vector field is a Yamabe soliton, then M is of constant negative curvature – α 2 . In this case, we see that the potential vector field is Killing. Next, we show that if the metric of a Riemannian manifold M admitting concurrent-recurrent vector field is a non-trivial r-quasi Yamabe gradient soliton with potential function f , then M has constant scalar curvature and is equal to – n ( n – 1) α 2 . Finally, an illustrative example is presented." @default.
- W4362508902 created "2023-04-06" @default.
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- W4362508902 date "2023-03-31" @default.
- W4362508902 modified "2023-10-14" @default.
- W4362508902 title "Yamabe Solitons and <i>τ</i>-Quasi Yamabe Gradient Solitons on Riemannian Manifolds Admitting Concurrent-Recurrent Vector Fields" @default.
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- W4362508902 doi "https://doi.org/10.1515/ms-2023-0037" @default.
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