Hypersurfaces of Metallic Riemannian manifolds as $k$-Almost Newton-Ricci solitons

Abstract

This research note is based on the study of $k$-Almost Newton-Ricci solitons ($k$-ANRS) immersing in metallic Riemannian manifold with the potential function $\psi: \mathcal{M}^{n} \rightarrow \mathcal{R}$.
Also, we obtain the minimal and totally geodesic conditions for hypersurface of metallic Riemannian manifold. Beside this, we show that hypersurfece $\mathcal{M}^{n}$ of metallic Riemannian manifold admits the steady $k$-Almost Newton-Ricci solitons. Beside this, we have explained some application of metallic Riemannian manifold admitting $k$-Almost Newton-Ricci solitons.