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In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.doi:10.32861/ajams.73.143.148 fatcat:4cymftqmtbckhpkjyotlx3aubi