A Note on Invariant Submanifolds of Metallic Riemannian Manifolds

Abstract

The goal of this paper is to examine invariant submanifolds in metallic Riemannian manifolds with the help of induced structures on them by the metallic Riemannian structure of the ambient manifold. We obtain a useful characterization of invariant submanifolds. Wealso discuss some necessary conditions for invariant submanifolds to be totally geodesic. Finally, we provide an example of an invariant submanifold.