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In this note, the generalized Lorentzian Sasakian-space-form M 1 2 n + 1 (f 1 , f 2 , f 3) satisfying certain constraints on the M -projective curvature tensor W * is considered. Here, we characterize the structure M 1 2 n + 1 (f 1 , f 2 , f 3) when it is, respectively, M -projectively flat, M -projectively semisymmetric, M -projectively pseudosymmetric, and φ − M -projectively semisymmetric. Moreover, M 1 2 n + 1 (f 1 , f 2 , f 3) satisfies the conditions W * (ζ , V 1) · S = 0 , W * (ζ , V 1) · R = 0 and W * (ζ , V 1) · W * = 0 are also examined. Finally, illustrative examples are given for obtained results. [ABSTRACT FROM AUTHOR]

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 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]

The present paper deals with a study of 3-dimensional contact metric generalized (κ, μ)-space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized (κ, μ)-space form with Q... = ...Q to be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric and ξ-projectively flat, respectively. [ABSTRACT FROM AUTHOR]

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 we study NMCP manifolds, which are (2p+2q+2)--dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the *--Ricci tensor. We prove that a *--Ricci-semi-symmetric NMCP manifold is *--Ricci-flat, and that a *--generalized quasi-Einstein NMCP manifold cannot be *--Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space. [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]