Generic Submanifolds Of Nearly Kaehler Manifolds

The first chapter introduces the background and the recent development, give an outline of main results of this dissertation.The second chapter introduces that the class of generic submanifold includes all real hypersurfaces, complex submanifolds. totally real submanifolds and CR-submanifolds. In this chapter we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamen-tal results in this chapte will be obtained.The third chapter discusses submersion of generic submanifolds of nearly Kaehler manifold. We prove that if π:M → B is a submersion of generic submanifold M of nearly Kaehler manifold M onto an almost Hermitian manifold B, then B is a nearly Kaehler manifold. We also obtain the decomposition theorems for such submersions and derive the relation between the holomorphic sectional curvatures of N and that of B.The fourth chapter intiate the study of totally real submanifolds of the near-ly Kaehler S3 × S3. we obtain the following results:let M be a complete totally real 2-dimensional submanifold of S3 × S3, then M is flat. And we will provide the conditions for M. to be minimal. Furthermore, for a 3-dimensional totally real submanifold of S3 × S3, we prove it is orientable and minimal. For a Lagrangian submanifolds of the nearly Kaehler S3 × S3, we provide conditions for a canonically induced almost contact metric structure by a unit vector field, to be α-Sasakian. Furthermore, assuming the almost contact metric structure is contact metric struc-ture, we show the conditions when the contact metric structure is Sasakian.The fifth chapter initiate the study of contact hypersurface in nearly Kaehler S3 × S3. There are three almost contact metric structures on a hypersurface of S3 × S3, we will give some important properties of them.