Semi-Symmetric Metric T-Connection in an Almost Contact Metric Manifold

In present paper, we studied the properties of semi-symmetric metric T−connection in almost contact metric manifolds. It has been shown that a generalised co-symplectic manifold with semi-symmetric metric T−connection is a generalised quasi-Sasakian manifold. Further, an almost contact metric manifold equipped with semi-symmetric metric T−connection is either projectively or con-circularly flat if and only if it is locally isometric to the hyperbolic space Hn(−1)