WARPED PRODUCT QUASI-HEMI-SLANT SUBMANIFOLDS OF METALLIC RIEMANNIAN MANIFOLDS

In this paper, we introduce the notion of warped product quasi-hemi-slant submanifolds within the framework of locally metallic Riemannian manifolds. We systematically classify all possible bipartite structural cases for these warped products and investigate their geometric existence. By evaluating totally geodesic and totally umbilical properties, we establish characterization theorems proving that specific configurations yield proper warped products, while others inherently reduce to trivial Riemannian products. Furthermore, we investigate the integrability conditions of the fundamental distributions, define rigorous boundary conditions for manifold reduction, and construct proper, non-trivial explicit examples in Euclidean space to guarantee the existence of such geometric structures.