On Metric Contact Pairs with Certain Semi-Symmetry Conditions

Blair et al. [7] introduced the notion of bicontact manifold in the context of Hermitian geometry. Bande and Hadjar [1] studied on this notion under the name of contact pairs. These type of structures have important properties and their geometry is some different from classical contact structures. In this paper, we study on some semi-symmetry properties of the normal contact pair manifolds. We prove that a Ricci semi-symmetric (or concircularly Ricci semi-symmetric) normal metric contact pair manifold is a generalized quasi-Einstein manifold. Also, we classify normal metric contact pair manifolds as a generalized quasi-Einstein manifold with certain semi-symmetry conditions L (X, Z).R = 0, R(X, Z).L = 0 and L (X, Z).L = 0 for the concircular curvature tensor L, the Riemannian curvature tensor R, and an arbitrary vector field X.