Almost $\eta$-Ricci and almost $\eta$-Yamabe solitons with torse-forming potential vector field

Abstract

We provide properties of almost $\eta$-Ricci and almost $\eta$-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold $\left(\widetilde{M},\widetilde{g} \right)$ whose potential vector field is the tangential component of a torse-forming vector field on $\widetilde{M}$, 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 $\eta$-Ricci or an almost $\eta$-Yamabe soliton in terms of the second fundamental tensor field.