The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.

The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.

We deal with compact KÃ¤hler manifolds M acted on by a compact Lie group K of isometries, whose complexification K has exactly one open and one closed orbit in M . If the K-action is Hamiltonian, we obtain results on the cohomology and the K-equivariant cohomology of M .

We classify isometric actions of compact Lie groups on quaternionic-KÃ¤hler projective spaces with vanishing homogeneity rank. We also show that they are not in general quaternion-coisotropic.

We study isometric actions of compact Lie groups on positive quaternionic-KÃ¤hler manifolds having all principal orbits 3coisotropic. We characterize them in terms of homeogeneity rank and give a classification of such actions on quaternionic projective spaces.

In the present paper we introduce the notion of complex asystatic Hamiltonian action on a KÃ¤hler manifold. In the algebraic setting we prove that if a complex linear group G acts complex asystatically on a KÃ¤hler manifold then the G-orbits are spherical. Finally we give the complete classification of complex asystatic irreducible representations.

We consider compact KÃ¤hler manifolds acted on by a connected compact Lie group K of isometries in a Hamiltonian fashion. We prove that the squared moment map ||Î¼|| is constant if and only if the manifold is biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact KÃ¤hler manifold which is acted on trivially by K. Theâ€¦ (More)