Pseudosymmetric contact metric manifolds in the sense of M. C. Chaki (Q2784827)

A Riemannian manifold is called pseudosymmetric of Chaki type if it is non-flat and if the first covariant derivative of its Riemann curvature tensor can be expressed using only the curvature tensor itself and some non-zero one-form according to a specific rule. It is called pseudo-Ricci-symmetric of Chaki type if its Ricci curvature tensor has such a property. In this paper, the authors derive properties for pseudosymmetric and pseudo-Ricci-symmetric manifolds of Chaki type for a special class of contact metric spaces (which includes Sasakian manifolds). However, a further calculation would have shown that such manifolds do not exist within this class.