1. The statement of theorems. Let G be a connected complex Lie group and let B be a closed complex Lie subgroup in G. The left coset space G/B is a complex manifold, which will be called a complex coset space. We denote by Bo the identity connected component of B and U the normalizer of BoThe canonical projection p of G/B onto G/ U defines a holomorphic fibre bundle, and the complex Lie group U...

In this paper, we begin a quantization program for nilpotent orbits OR of a real semisimple Lie group GR. These orbits arise naturally as the coadjoint orbits of GR which are stable under scaling, and thus they have a canonical symplectic structure ω where the GR-action is Hamiltonian. These orbits and their covers generalize the oscillator phase space T R, which occurs here when GR = Sp(2n,R) ...

In [4] B. Y. Chen studied warped product CR-submanifolds in Kaehler manifolds. Afterward, I. Hasegawa and I. Mihai [5] obtained a sharp inequality for the squared norm of the second fundamental form for contact CR-warped products in Sasakian space form. Recently Alegre, Blair and Carriago [1] introduced generalized Sasakian space form. The aim of present paper is to study contact CR-warped prod...

Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are obtained by complex submanifolds via a generalization of the so called hyperkaehler rotation trick; thus they retain part of the rigidity of the complex submanifolds: indeed all special Lagrangian submanifolds of X turn out to...