The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained.

The index theorem for a harmonic mapping of riemannian manifolds is given. Let /: M -> N be a holomorphic mapping of Kaehler manifolds. Then it is shown that the index of / is zero and that a Jacobi field along/is a holomorphic section of the bundle f*T(N) induced by/.

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP n and Cn.

Cosymplectic manifolds provide a natural setting for time dependent mechanical systems as they are locally product of a Kaehler manifold and a one dimensional manifold. Thus study of warped product submanifolds of cosymplectic manifolds is significant. In this paper we have proved results on the non-existence of warped product submanifolds of certain types in cosymplectic manifolds. M.S.C. 2000...

In a previous paper we built a modified Hamiltonian formalism to make possible explicit maps among manifolds. In this paper the modified formalism was generalized. As an application, we have built maps among spaces associated to spinors, as well as maps among Kaehler spaces. ∗ E-mail: [email protected]

Recently, Sahin [10] studied the anti-invariant Riemannian submersions from almost Hermitian manifolds onto manifolds. In present work, these notions of and Lagrangian have been extended to locally conformal Kaehler Certain decomposition results geometry foliation also investigated.

We provide models that are as close possible to being formal for a large class of compact manifolds admit transversely Kaehler structure, including Vaisman and quasi-Sasakian manifolds. As an application we able classify the corresponding nilmanifolds.

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and space form. We give inequalities for the length of second fundamental form mean curvature and, using Gauss Codazzi equations, get many useful results