CERTAIN RESULTS OF RICCI-YAMABE SOLITONS ON $(LCS)_N$-MANIFOLDS

Jay Prakash Singh, Chhakchhuak Zosangzuala

DOI Number
https://doi.org/10.22190/FUMI220606055S
First page
797
Last page
812

Abstract


The goal of this paper is to characterize Lorentzian concircular structure manifolds (briefly, $(LCS)_n$-manifolds) admitting Ricci-Yamabe solitons. It is shown that an $(LCS)_n$-manifold which admits the Ricci-Yamabe soliton becomes flat when the soliton is steady. Next, we construct a $3$-dimensional and $5$-dimensional $(LCS)_n$-manifold satisfying the result. Also, the expression for the scalar $\lambda$ on an $(LCS)_n$-manifold admitting conformal Ricci-Yamabe soliton is obtained. Lastly, we extend our study to $\eta-$Ricci-Yamabe soliton on a conformally flat $(LCS)_n$ $(n\geq4)$ manifold in which we have shown the condition when the soliton is shrinking, steady and expanding with $\xi$ being a torse forming vector field.

Keywords

Ricci-Yamabe solitons, torse forming, conformally flat, $(LCS)_n-$manifolds.

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DOI: https://doi.org/10.22190/FUMI220606055S

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