Characterizations of various curvatures on weakly symmetric Ka¨hler manifolds

Abstract

The objective of the present paper is to introduce a special type of semi-symmetric metric connection ∇∗ on weakly symmetric K¨ ahler manifolds to reduce the manifold, which is Einstein and Ricci flat. Also, we use a non-flat Riemannian manifold called a weakly concircular symmetric manifold and study its geometric properties on a weakly symmetric K¨ ahler manifold endowed with a special type of semisymmetric metric connection that satisfies several relations on 1-form, differential equations, recurrent space, and Einstein manifold.