Totally Umbilical Semi-Invariant Submanifolds in Locally Decomposable Metallic Riemannian Manifolds

Abstract

In this paper, we obtain some classification theorems for totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no totally umbilical proper semi-invariant submanifolds in a posivitely or negatively curved locally decomposable metallic Riemannian manifold.