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In this paper we study the conservative conformal curvature tensor and the conservative quasi-conformal curvature tensor on a trans-Sasakian manifold with respect to a semi-symmetric metric connection. It is shown that a trans-Sasakian manifold with conservative conformal curvature tensor is an Einstein manifold, and with quasi-conformal curvature tensor is an η-Einstein manifold. [ABSTRACT FROM AUTHOR]

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant φ-sectional curvature, and prove the structure theorem for ξ-conformally flat and φ-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an η-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature ε. [ABSTRACT FROM AUTHOR]