Аннотация:
Hamiltonian minimality (H-minimality) for Lagrangian submanifolds
is a symplectic analogue of minimality in Riemannian geometry. A
Lagrangian immersion is called H-minimal if the variations of its
volume along all Hamiltonian vector fields are zero.
We study the topology of H-minimal Lagrangian submanifolds $N$ in
$\mathbb C^m$ constructed from intersections of real quadrics in
the work of Mironov. This construction is linked via an embedding
criterion to the well-known Delzant construction of Hamiltonian
toric manifolds.
By applying the methods of toric topology we produce new examples
of H-minimal Lagrangian submanifolds with quite complicated
topology. The interpretation of our construction in terms of
symplectic reduction leads to its generalisation providing new
examples of H-minimal submanifolds in toric varieties.
The talk is based on a joint work with Andrey E. Mironov.