STUDY OF DIFFERENT TYPES OF CONNECTION IN VARIOUS DIFFERENTIABLE MANIFOLD

Abstract

Abstract: The present work investigates numerous types of affine connections defined on differentiable manifolds, with a focus on Lorentzian para-Sasakian (LP-Sasakian) manifolds with non-Levi-Civita structures. We construct explicit equations for the related torsion, curvature, Ricci tensor, and scalar curvature by adding a semi-symmetric non-metric connection that is consistent with the underlying LP-Sasakian structure, illuminating their differences from traditional Riemannian equivalents. The paper rigorously describes generalized pseudo Ricci symmetric, generalized Ricci-recurrent, semi-pseudo symmetric, and semi-pseudo Ricci symmetric manifolds using covariant differential constraints on curvature and Ricci tensors. Several structural theorems are established utilizing tensorial identities, Bianchi-type relations, and contraction techniques, revealing that generalized Ricci-recurrent LP-Sasakian manifolds admitting Codazzi or cyclic type Ricci tensors necessarily reduce to Einstein manifolds under the considered connection.Furthermore, the non-existence of semi-pseudo symmetric and semi-pseudo Ricci symmetric LP-Sasakian manifolds (for dimension