Concircularly semi-symmetric metric connection

Abstract

Results on a concircularly semi-symmetric metric connection on a Riemannian manifold are presented. Six linearly independent curvature tensors with respect to this non-symmetric linear connection are studied, and the tensors coincident with the Weyl projective curvature  tensor and the concircular curvature tensor of the Levi-Civita connection are determined. Transformations of connections when the  Riemannian curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are  invariant are also observed. Moreover, new conditions for the Einstein manifold are derived.