Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey

Abstract

We provide a brief survey on the properties of submanifolds in metallic Riemannian manifolds. We focus on slant, semi-slant and hemi-slant submanifolds in metallic Riemannian manifolds and, in particular, on invariant, anti-invariant and semi-invariant submanifolds. We also describe the warped product bi-slant and, in particular, warped product semi-slant and warped product hemi-slant submanifolds in locally metallic Riemannian manifolds, obtaining some results regarding the existence and nonexistence of non-trivial semi-invariant, semi-slant and hemi-slant warped product submanifolds. We illustrate all these by suitable examples.

Keywords

• metallic Riemannian manifold
• warped product submanifold
• slant
• semi-slant
• hemi-slant
• bi-slant submanifold