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Abstract. The object of the present paper is to study a semi-symmetric metric connection in an (ε)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (ε)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.

Abstract:The object of the present paper is to study a semi-symmetric non-metric connection in an indefinite para Sasakian manifold. In this paper, we obtain the relation between the semi-symmetric non-metric connection and Levi-Civita connection in an indefinite para Sasakian manifold. Also, the Nijenhuis tensor, curvature tensor and projective curvature tensor of semi-symmetric non-metric connection in an indefinite para Sasakian manifold have been studied.

The object of the present paper is to generalize pseudo-projective curva-ture tensor of para-Kenmotsu manifold with the help of a new generalized(0,2) symmetric tensorZintroduced by Mantica and Suh. Various geo-metric properties of generalized pseudo-projective curvature tensor of para-Kenmotsu manifold have been studied. It is shown that a generalized pseudo-projectivelyφ-symmetric para-Kenmotsu manifold is an Einstein manifold

In this paper, relation between curvature tensors of Levi-Civita connection and Zamkovoy connection on para-Kenmotsu manifolds have been obtained.Quasi M-projectively flat, M-projectively flat and φ-M-projectively flat paraKenmotsu manifolds admitting Zamkovoy connection have been studied. Also, para-Kenmotsu manifolds admitting Zamkovoy connction satisfying M¯ (ξ, U).R¯ = 0 and M¯ (ξ, U).S¯ = 0 have been developed