Kenmotsu Manifold Oblique Submanifolds And Semi-oblique Sub-manifold,

At the beginning of 1990s, B. Y. Chen defined and studied slant immersions in complex geometry as a natural generalization of both holomorphic immersions and totally real immersions (see [16]). Later many authors have studied such slant immersions in almost Hermitian manifolds. In [17]and[18], J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez have studied and characterized slant submanifolds of Sasakian manifolds and they have given some interesting examples of such immersions. Moreover, in [19], they have presented existence and uniqueness theorems for slant immersions into Sasakian space forms, which are similar to that of B. Y. Chen and L. Vrancken in complex geometry [20].Recently, in [15] N. Papaghiuc has introduced a class of submanifolds in an almost Hermitian manifold, called the semi-slant submanifolds. In [21],J. L. Cabrerizo, A. Car-riazo, L. M. Fernandez and M. Fernandez have studied the semi-slant submanifold of Sasakian manifold,many geometric results has been obtained.In 1972,K. Kenmotsu introduced another class of almost contact Riemannian manifold,called Kenmotsu manifold.Kenmotsu manifold is so close to Sasakian manifold in structure that there might be some same characteristics in both manifold.In the present paper,we introduced and studied slant submanifold and semi-slant submanifold of Kem-motsu manifold and we get the following main results:Theoreml. Let M be a semi-slant submanifold of a Kenmotsu manifold M such that d1 0, the distribution D1 is not integrable.Theorem2 . Let M be a semi-slant submanifold of a Kenmotsu manifold M. Then the slant distribution D2 is not integrable.Theorems. Let M be a semi-slant submanifold of a Kenmotsu manifoldM. Then, we have:(i) The distribution D1 < >is integrable if and only if(ii) The distribution D2 < >is integrable if and only if...