arXiv subjects
Publications and source records attributed to Fabio Podesta.
In the present paper we introduce the notion of complex asystatic Hamiltonian action on a Kähler manifold. In the algebraic setting we prove that if a complex linear group $G$ acts complex asystatically on a Kähler manifold then the $G$-orbits are spherical. Finally we give the complete classification of complex asystatic irreducible representations.
The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.
We deal with seven dimensional compact Riemannian manifolds of positive curvature which admit a cohomogeneity one action by a compact Lie group G. We prove that the manifold is diffeomorphic to a sphere if the dimension of the semisimple part of G is bigger than 6.
We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on isometrically by a non semisimple Lie group with an hypersurface orbit.