Gauge field theory in terms of complex Hamiltonian geometry.
Generalized PN manifolds and separation of variables
The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.
Geometry and analytic theory of Frobenius manifolds.
Geometry of parallelizable manifolds in the context of generalized Lagrange spaces.