In this paper, we discuss submersion of CR-submanifolds of locally conformal Kaehler manifold. We prove that if π : M −→ B◦ is a submersion of CR-submanifold M of a locally conformal Kaehler manifoldM onto an almost Hermitian manifold B◦, then B◦ is a locally conformal Kaehler manifold. Furthermore, we discuss totally umbilical CR-submanifold and cohomology of CR-submanifold of locally conforma...

In this paper, we study pseudo-slant submanifolds of nearly Kaehler manifolds. A classification theorem on a totally umbilical pseudo-slant submanifold of a nearly Kaehler manifold is proved. 2000 Mathematics Subject Classification: 53C40, 53B25, 53C15.

In this paper I construct, using off the shelf components, a compact symplectic manifold with a non-trivial Hamiltonian circle action that admits no Kaehler structure. The non-triviality of the action is guaranteed by the existence of an isolated fixed point. The motivation for this work comes from the program of classification of Hamiltonian group actions. The Audin-Ahara-Hattori-Karshon class...

In this paper, we study warped product pseudo-slant submanifolds of nearly Kaehler manifolds. We prove the non-existence results on warped product submanifolds of a nearly Kaehler manifold.

We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial Kaehler-Ricci solitons (KRS), both complete and complete, which can be Kaehler immersed into infinite dimensional complex space forms. This result shows that the triviality a KRS induced by finite form proved in [12] does hold when ambient is allowed to dimensional. Moreover, we show potential non-elliptic necessarily defined...

Recently, the present authors considered doubly warped product CR-submanifolds in a locally conformal Kaehler manifold and got some inequalities about the length of the second fundamental form ([14]). In this report, we obtain an inequality of the mean curvature of a doubly warped product CR-submanifold in a locally conformal Kaehler space form. Then, we consider the equality case of this inequ...

Given a Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: eg, finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal Lagrangian orbits are isolated.

In this paper we introduce the notion of screen pseudo-slant lightlike submanifolds of indefinite Kaehler manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen pseudo-slant lightlike submanifolds of an indefinite Kaehler manifold have been obtained. Further, we obtain necessary and suff...

We obtain a characterization for a compact Hopf hypersurface in the nearly Kaehler sphere S using a pinching on the scalar curvature of the hypersurface. It has been also observed that the totally geodesic sphere S in S has induced Sasakian structure as a hypersurface of the nearly Kaehler sphere S. M.S.C. 2000: 53C20, 53C45.

The Riemannian submersions of a CR-hypersurface M of a Kaehler-Einstein man-ifold˜M are studied. If M is an extrinsic CR-hypersurface of˜M, then it is shown that the base space of the submersion is also a Kaehler-Einstein manifold. 1. Introduction. The study of the Riemannian submersions π : M → B was initiated by O'Neill [14] and Gray [9]. This theory was very much developed in the last thirty...