Homogeneous Lagrangian submanifolds (Q947305)

Let \(K\) be a compact connected group of isometries acting in a Hamiltonian fashion on a compact Kähler manifold \(M\). The authors find necessary and sufficient conditions for \(M\) to admit a \(K\) - homogeneous Lagrangian submanifold. Also, they analyse the minimality of Lagrangian submanifolds of \(M\). Finally, a classification of simple groups is given acting on the complex projective space with a Lagrangian orbit, resulting in an explicit list of these orbits.