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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]

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]