Some curvature conditions on a para-Sasakian manifold with canonical paracontact connection
Summary: We study a canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to the canonical paracontact connection is an \(\eta\)-Einstein manifold. We also investigate some properties of the curvature tensor, the conformal curvature tensor, the \(W_2\)-curvature tensor, the concircular curvature tensor, the projective curvature tensor, and the pseudo-projective curvature tensor with respect to the canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to the canonical paracontact connection is of constant scalar curvature. We give some characterizations of pseudo-projectively flat para-Sasakian manifolds.
scientific article; zbMATH DE number 6137709
scientific article