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In the present paper, we have studied the curvature tensors of PSasakian manifold. For a P-Sasakian manifold, W1 ·S = 0, W1 · e Z = 0 and W9 · W1 = 0 cases are considered. According these cases, PSasakian manifolds have been characterized such as η-Einstein and Einstein. In addition, we research W1-flat and W9-flat for a PSasakian manifold. The results are interesting and give an idea about the geometry of P-Sasakian manifold. [ABSTRACT FROM AUTHOR]

In this paper we present invariant submanifolds of an almost α-cosymplectic (k, µ, ν)-space. Then, we gave some results for an invariant submanifold of an almost α-cosymplectic (k, µ, ν)-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic (k, µ, ν)-space. [ABSTRACT FROM AUTHOR]

In this paper, some properties of Lorentz para-Kenmotsu manifolds are studied using specified curvature tensors. The Lorentz para-Kenmotsu manifold is investigated in terms of the curvature tensors W 8 and W 9 . Initially, the tensor-based characterization of semisymmetric Lorentz para-Kenmotsu manifolds is studied. Subsequently, we consider the Lorentzian para-Kenmotsu manifold, which admits almost η -Ricci solitons via these curvature tensors. According to the W 8 and W 9 curvature tensors, Ricci pseudosymmetry notions of Lorentzian para-Kenmotsu manifolds accepting η -Ricci soliton have been developed. Following that, required conditions for the Lorentzian para-Kenmotsu manifold, admitting η -Ricci soliton to be Ricci semisymmetric, are presented based on the curvature tensors chosen. Further, various characterizations are provided, and classifications are made under certain conditions. Finally, the characterizations of the invariant submanifolds of Lorentz para-Kenmotsu manifold on the W 8 and W 9 curvature tensors are investigated. We obtained the necessary and sufficient conditions for an invariant submanifold of a para-Kenmotsu to be W 8 and W 9 pseudoparallel. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of the pseudo-slant submanifolds of a cosymplectic space form. Necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, pseudo-slant product, mixed geodesic and totally geodesic in cosymplectic manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifold in a cosymplectic manifold and cosymplectic space form.

In this paper, we consider Lorentz generalized Sasakian space forms admitting almost η--Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of Lorentz generalized Sasakian space forms admitting η--Ricci soliton have introduced according to the choice of some special curvature tensors such as Riemann, concircular, projective, M--projective, W1 and W2: Then, again according to the choice of the curvature tensor, necessary conditions are given for Lorentz generalized Sasakian space form admitting hRicci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made. [ABSTRACT FROM AUTHOR]

In this article, semi-symmetry of almost C (α)-manifold is investigated on some special curvature tensors. First, the behavior of the almost C (α)-manifold is investigated when the special curvature tensors discussed are flat. Then, for these special curvature tensors, the behavior of the manifold in the semi-symmetric condition is observed and for some special curvature tensors, important properties such as the semi-symmetric almost C (α)-manifold being Einstein and η-Einstein manifold are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider pseudosymmetric Lorentz Sasakian space forms admitting almost η-Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of Lorentz Sasakian space forms admits η-Ricci soliton have introduced according to the choice of some special curvature tensors such as Riemann, concircular, projective, M-projective, W1 and W2: Then, again according to the choice of the curvature tensor, necessary conditions are given for Lorentz Sasakian space form admits η-Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made under the some conditions. [ABSTRACT FROM AUTHOR]

In this article, pseudoparallel submanifolds for almost Kenmotsu (κ, μ, ν) --space are investigated. The almost Kenmotsu (κ, μ, ν) --space is considered on the concircular curvature tensor. Submanifolds of these manifolds with properties such as concircular pseudoparallel, concircular 2--pseudoparallel, concircular Ricci generalized pseudoparallel, and concircular 2--Ricci generalized pseudoparallel has been characterized. Necessary and sufficient conditions are given for the invariant submanifolds of almost Kenmotsu (κ, μ, ν) --space to be total geodesic according to the behavior of the κ, μ, ν functions. [ABSTRACT FROM AUTHOR]

The purpose of this study is to characterize Kenmotsu manifolds that satisfy specific curvature conditions. We give the Kenmotsu manifold curvature tensors satisfying the conditions R.W5 = 0, R.W7 = 0, R.W9 = 0 and R.W* 0 = 0. Also, we consider the Kenmotsu metric manifold a W*0-flat and a-W*0-flat. As a result, M is an n-Einstein Kenmotsu metric manifold. [ABSTRACT FROM AUTHOR]

In this article, some special curvature conditions created by the W*0 -curvature tensor with the Riemann, Ricci, projective, concircular, quasiconformall curvature tensors in 3-dimensional para-Sasakian manifold are discussed. In addition, the behavior of the para-Sasakian manifold is investigated by considering the atness, semi-symmetry, pseudo-symmetry and Ricci pseudo-symmetry properties of the W*0 -curvature tensor. [ABSTRACT FROM AUTHOR]

In this paper we present the curvature tensors of Kenmotsu manifold satisfying the conditions R(X; Y). W0 = 0, R(X; Y). W1 1 = 0, R(X; Y). W1 = 0, R(X; Y). W3 = 0 and R(X; Y). W4 = 0. According these cases, Kenmotsu manifolds have been characterized. I think that some interesting results on a Kenmotsu metric manifold are obtained. [ABSTRACT FROM AUTHOR]