This paper investigates the new curvature properties of warped product manifolds (WPM) with a semi-symmetric metric connection (SSMC) and its implications for General Relativity (GR) and modern theories of gravity. Warped product manifolds offer a useful geometric setting for many diverse classes of space-time structures such as cosmological and black-hole solutions. The models may explain both intrinsic spin effects and nonequilibrium phenomena associated with the underlying structure of matter because we substitute an SSMC for the conventional Levi-Civita connection (LCC) while preserving metric compatibility & naturally adding torsion. This link may be used to formally express the Riemann curvature tensor (CT), Ricci tensor, scalar curvature, & sectional curvature of WPM. We also prove that these manifolds must be Einstein (also known as conformally flat) in order for them to be. We pay special attention to Robertson–Walker space-times and the way torsion modifies their geometric and physical properties. We give some illustrative examples to show the applicability of our theoretical results and applicability of the derived forms. The resulting curvature identities generalize their classical counterparts for the Levi-Civita connection, while uncovering new geometric characteristics introduced by torsion. Thus, the results provide a more general mathematical basis for research on curved space-times, and also contribute to our understanding of geometric structures arising in differential geometry, mathematical physics, cosmology and alternative by gravity.