Geometrical and physical properties of W2-symmetric and -recurrent manifolds

Abstract

The authors discuss mainly that the Riemannian manifold Mn admitting a unit preserving circle field ? in the present paper. A sufficient and necessary condition is given that Riemannian manifold Mn is an Einstein manifold by imposing some conditions on W2 curvature tensor. Further, this paper obtains the algebra representation of curvature tensors of a W2-recurrent Riemannian manifold Mn given by R???? = 1/d2 [d?d?R?? ? d?d?R?? + d?d?R?? ? d?d?R??].