An Optimal Inequality for the Normal Scalar Curvature in Metallic Riemannian Space Forms

Abstract

In this paper, we prove the DDVV conjecture for a slant submanifold in metallic Riemannian space forms with the semi-symmetric metric connection. The equality case of the derived inequality is discussed, and some special cases of the inequality are given.

Keywords

• metallic structure
• Riemannian manifolds
• scalar curvature
• Wintgen inequality