$\star$-Ricci-Yamabe solitons on almost coK\"{a}hler manifolds

Year 2025, Early Access, 1 - 20

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 coK\"{a}hler 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 coK\"{a}hler manifold admitting $\star$-Ricci-Yamabe soliton under certain restriction on $\star$-scalar curvature is coK\"{a}hler and $\star$-Ricci flat; in addition, that the soliton is steady. $(\kappa, \mu)$-almost coK\"{a}hler manifolds admitting such solitons are also considered and finally, the obtained results are supported by non-trivial examples.

Keywords

Almost coK\"{a}hler manifold, $(\kappa, \mu)$-nullity distribution, $\star$-Ricci curvature, Ricci soliton, Yamabe soliton

References

• [1] J.E. Andersen, Geometric quantization of symplectic manifolds with respect to reducible non-negative polarization, Commun. Math. Phys., 183, 401–421, 1997.