Chen’s inequality for Hemi-slant warped products in locally Metalic Riemannian manifolds

Abstract

Cristina-Elena and Adara-Monica have previously begun studying warped product hemi-slant submanifolds in metallic Riemannian manifolds. In the present study, we extend their work by studying warped product hemi-slant submanifolds of two specific forms: M = Mθ ×f M⊥ and M = M⊥ ×f Mθ, where M⊥ and Mθ are anti-invariant and proper slant submanifolds of a metallic Riemannian manifold and f is a warping function. We give examples of warped product hemi-slant submanifolds and establish a sharp inequality for the squared norm of the second fundamental form of warped product hemi-slant submanifolds in metallic Riemannian manifolds. We also consider the equality case.