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In this article, the M-projective and Weyl curvature tensors on a normal paracontact metric manifold are discussed. For normal paracontact metric manifolds, pseudosymmetric cases are investigated and some interesting results are obtained. We show that a semisymmetric normal paracontact manifold is of constant sectional curvature. We also obtain that a pseudosym-metric normal paracontact metric manifold is an η-Einstein manifold. Finally, we support our topic with an example. [ABSTRACT FROM AUTHOR]

In this article, the behavior of the C(α)-manifold satisfying the conditions R(X,Y)W* = 0,W* (X,Y)R = 0,W* (X,Y) Z = 0, W* (X,Y)S = 0 and W* (X,Y) C = 0 on the M--projective curvature tensor is investigated. The C(α)--Manifold is characterized according to these states of the curvature tensor. Here, W*,R,S, Z and C are M--projective, Riemann, Ricci, concircular and quasiconformal curvature tensors. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study (k,μ)-Paracontact metric manifold. We introduce the curvature tensors of (k,μ)-Paracontact manifold satisfying the conditions W*0 (X,Y)·P = 0, W*0 (X,Y)·R = 0, W*0 (X,Y)·Z= 0, W*0 (X,Y)·S = 0 and W*0 (X,Y)·Ce = 0. According these cases, (k,μ)-Paracontact manifolds have been characterized. In my opinion some exciting results on a (k,μ)- Paracontact metric manifold are obtained. [ABSTRACT FROM AUTHOR]

In the present paper, we have studied the curvature tensors of a normal almost paracontact metric manifold satisfying the conditions C̃(ξ,U1)R = 0, C̃(ξ,U1)P = 0, C̃(ξ,U1) Z̃ = 0, C̃(ξ,U1)S = 0 and C̃(ξ,U1)C̃= 0. According these cases, we classified normal almost paracontact metric manifolds, where R is the Riemanniann curvature tensor, C̃ is the quasi-conformal curvature tensor, Pis the projective curvature tensor, Z̃ is the concircular curvature tensor and S is the Ricci tensor. [ABSTRACT FROM AUTHOR]

In this paper, we study the pseudo-slant submanifolds of a nearly Sasakian manifold. We characteterize a totally umbilical properpseudo-slant submanifolds and find that a necessary and sufficient condition for such sub-manifolds totally geodesic. Also the integrability conditions of distributions of pseudo-slant submanifolds of a nearly Sasakian manifold are investigated. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give neces- sary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product sub- manifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study generalized Sasakianspace- forms with the conditions satisfying e C(ξ,X) e C = 0, e C(ξ,X)R = 0, e C(ξ,X)S = 0 and e C(ξ,X)P = 0. According these cases, generalized Sasakianspace forms have been classified. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study (LCS)n-manifolds with vanishing quasi-conformal curvature tensor. (LCS)n-manifolds satisfying Ricci-symmetric condition are also characterized. [ABSTRACT FROM AUTHOR]

In this paper, we research the existence or non-existence of warped product semi-slant submanifolds in Kenmotsu manifolds. Consequently, we see that there are no proper warped product semi-slant submanifolds in Kenmotsu manifolds such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant), respectively. [ABSTRACT FROM AUTHOR]

In this article we investigate the geometry of CR-lightlike submanifolds in an indefinite Kähler product manifold. In particular, we obtain the necessary and sufficient conditions for a CR-lightlike submanifold in an indefinite Kähler product manifold to be either CR-lightlike product, or D-geodesic, or D'-geodesic. We also study totally umbilical and curvature-invariant CR-lightlike submanifolds in ...1(c1) × ...2(c2). [ABSTRACT FROM AUTHOR]

In this article, we give a necessary and sufficient condition for warped product semi-invariant submanifolds to be Riemannian product semi-invariant submanifolds in a locally Riemannian product manifold whose factor manifolds are real space form. [ABSTRACT FROM AUTHOR]

In this paper, the geometry of CR-submanifolds of a Kaehler product manifold is studied. Fundamental of these submanifolds are investigated such as CR-product, pseudo-umbilical and curvature-invariant. Finally, we show that there exists no totally umbilical CR-submanifold in a Kaehler product manifold M = M1(c1) ×M2(c2). [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold. Fundamental properties of these type submanifolds such as the integrability of the distributions D, D\bot and mixed-geodesic property are studied. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D\bot-geodesic. [ABSTRACT FROM AUTHOR]

In this paper, the geometry of F-invariant submanifolds of a Kaehlerian product manifold is studied. The fundamental properties of these submanifolds are investigated such as pseudo umbilical, curvature invariant, totally geodesic, mixed geodesic submanifold and locally decomposable Riemannian product manifold. [ABSTRACT FROM AUTHOR]