$\star$-Ricci-Yamabe solitons on almost coKähler manifolds

Year 2025, Volume: 54 Issue: 3, 874 - 893, 24.06.2025

U.c. De , Adara M. Blaga , Avijit Sarkar , Tarak Mandal

https://doi.org/10.15672/hujms.1357924

Abstract

The aim of the present article is to analyze $\star$-Ricci--Yamabe solitons on almost coKähler manifolds and to characterize them when the potential vector field is pointwise collinear with the Reeb vector field. It is proved that a compact almost coKähler manifold admitting a $\star$-Ricci--Yamabe soliton under certain restriction on $\star$-scalar curvature is coKähler and $\star$-Ricci flat; in addition, that the soliton is steady. $(\kappa, \mu)$-almost coKähler manifolds admitting such solitons are also considered and finally, the obtained results are completed by non-trivial examples.

Keywords

almost coKähler manifold , $(\kappa$ , $\mu)$-nullity distribution , $\star$-Ricci curvature , Ricci soliton , Yamabe soliton

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