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The paper deals with the study of M-projective curvature tensor on (κ, μ)-contact metric manifolds. We classify non-Sasakian (κ, μ)-contact metric manifold satisfying the conditions R(ξ,X) ·M = 0 and M(ξ,X) · S = 0, where R and S are the Riemannian curvature tensor and the Ricci tensor, respectively. Finally, we prove that a (κ, μ)-contact metric manifold with vanishing extended M-projective curvature tensor Me is a Sasakian manifold. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study weakly symmetries of Kenmotsu manifolds with respect to quarter-symmetric metric connection. We investigate the properties of weakly symmetric, weakly Ricci-symmetric and weakly concircular Ricci-symmetric Kenmotsu manifolds with respect to quarter symmetric metric connection and obtain interesting results. [ABSTRACT FROM AUTHOR]

The object of this paper is to study (k, µ)-para contact metric manifolds with qusi-conformal curvature tensor. It has been shown that, h-quasi conformally semi-symmetric and φ-quasi-conformally semi-symmetric (k, µ)-paracontact metric manifold with k ≠ - 1 cannot be 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]