Anna Gori

Coisotropic and Polar actions on Complex Grassmannians

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.

A splitting result for compact symplectic manifolds

We consider compact symplectic manifolds acted on effectively by a compact connected Lie group K in a Hamiltonian fashion. We prove that the squared moment map ∥μ∥2 is constant if and only if K is semisimple and the manifold is K-equivariantly symplectomorphic to a product of a flag manifold and a compact symplectic manifold which is acted on trivially by K. In the almost-Kähler setting the symplectomorphism turns out to be an isometry.

Isometric embeddings of Kähler-Ricci solitons in the complex projective space

We prove that a compact complex manifold endowed with a nontrivial Kahler-Ricci soliton cannot be isometrically embedded in the FubiniStudy complex projective space as a complete intersection.