A New Algebraic Inequality and Some Applications in Submanifold Theory

Abstract

We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

Keywords

• Riemannian space form
• submanifold
• Chen invariants
• Chen inequalities
• statistical manifold
• statistical submanifold