Slant submanifolds of Golden Riemannian manifolds

Abstract

In this paper, we study slant submanifolds of Riemannian manifolds with Golden structure. A Riemannian manifold $(\tilde{M},\tilde{g},\phi )$ is called a Golden Riemannian manifold if the $(1,1)$ tensor field $\phi$ on $\tilde{M}$ is a golden structure, that is ${\phi }^2=\phi +I$ and the metric $\tilde{g}$ is $\phi -$ compatible. First, we get some new results for submanifolds of a Riemannian manifold with Golden structure. Later we characterize slant submanifolds of a Riemannian manifold with Golden structure and provide some non-trivial examples of slant submanifolds of Golden Riemannian manifolds.