INVARIANT SUBMANIFOLDS IN GOLDEN RIEMANNIAN MANIFOLDS

Abstract

In this paper, we study invariant submanifolds of a golden Rie- mannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold. We demonstrate that any invariant sub- manifold in a locally decomposable golden Riemannian manifold leaves invari- ant the locally decomposability of the ambient manifold. We give a necessary and sufficient condition for any submanifold in a golden Riemannian manifold to be invariant. We obtain some necessary conditions for the totally geodes- icity of invariant submanifolds. Moreover, we find some facts on invariant submanifolds. Finally, we present an example of an invariant submanifold.