Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection

Abstract EN

We study canonical paracontact connection on a para-Sasakian manifold.

We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold.

We also investigate some properties of curvature tensor, conformal curvature tensor, W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold.

It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature.

We give some characterizations for pseudo-projectively flat para-Sasakian manifolds.