Hamiltonian minimal Lagrangian cones in \(\mathbb C^m\) (Q2566545)

The author gives a correspondence between a Hamiltonian Lagrangian cone in \(\mathbb C^n\), a Legendrian minimal submanifold in the unit sphere and a Hamiltonian Lagrangian submanifold in the complexe projective space. As an Application of this result he proves that a Hamiltonian minimal Lagrangian cone in \(\mathbb{C}^n\) such that the first Betti number of its link is zero must be a special Lagrangian cone. Moreover he constructs more examples of Hamiltonian minimal (nonminimal) Lagrangian cones and studies their stabilities.