Hsu-unified structure manifold coupled with a generalized Wintgen type inequality

Abstract

The goal of this research note is that, H$su$-unified structure manifolds with a semi-symmetric non-metric S-connection has been investigated. The Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature of the H$su$-unified structure manifold with a semi-symmetric non-metric S-connection are transformed into their respective formulations. Mainly, we derive the generalized Wintgen inequalities for submanifolds in H$su$-unified structure manifolds with a semi-symmetric non-metric S-connection. In addition, we discuss the Wintgen inequality for totally umbilical submanifolds of H$su$-unified structure manifolds with a semi-symmetric non-metric S-connection. Also, we deduce the same inequality for the almost complex manifold, almost tangent manifold, almost product manifold and GF-manifold, and $\pi$-structure ambient manifolds. Finally, we deduced a universal lower bound of the norms of specific functions involving scalar curvature, normalized scalar curvature, and mean curvature to establish topological obstructions for submanifolds in H$su$-unified structure manifolds with a semi-symmetric non-metric S-connection.