Almost η-Ricci and almost η-Yamabe solitons with torse-forming potential vector field

2020/03/29 by Adara M. Blaga, Blaga, Adara M., Cıhan Özgür +1 · 2 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · doi:10.48550/arxiv.2003.12574

Abstract

We provide properties of almost η-Ricci and almost η-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold (\widetildeM,\widetildeg ) whose potential vector field is the tangential component of a torse-forming vector field on \widetildeM, treating also the case of a minimal or pseudo quasi-umbilical hypersurface. Moreover, we give necessary and sufficient conditions for an orientable hypersurface of the unit sphere to be an almost η-Ricci or an almost η-Yamabe soliton in terms of the second fundamental tensor field.

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