The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...

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...

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...

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, 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.

Warped product manifolds provide excellent setting to model space-time near black holes or bodies with large gravitational force (cf. [1], [2], [14]). Recently, results are published exploring the existence (or non-existence) of warped product submanifolds in Kaehlerian and contact settings (cf. [6], [17], [20]). To continue the sequel, we have considered warped product submanifolds of nearly K...