Some Novel Results on (α, β)-Ricci-Yamabe Soliton and its Spacetime
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Abstract
This article aims to investigate the characteristics of $(\alpha,\beta)$-Ricci-Yamabe Soliton (briefly: $(\alpha,\beta)-(RYS)_n$) and its spacetime. The inclusion of killing vector field and the Lorentzian metrics make the Ricci-Yamabe soliton richer and interesting. We study the cosmological and dust fluid model on $(RYS)_4$ equipped with Lorentzian para Sasakian $(LPS)_4$ spacetime. The cases of $\eta$-parallel Ricci tensor and the Poisson structure have been studied on $(RYS)_n$ equipped with $(LPS)_n$ manifold. Gradient $(RYS)_n$ equipped with $(LPS)_n$ manifold also reveal. Finally, we establish an example of four-dimensional LP-Sasakian manifold $(LPS)_4$ that satisfy $(\alpha,\beta)-(RYS)_4$ and some results.
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