Real Monge-Ampère operators and (almost) complex structures. Part 2

We observe some interesting geometric structures which are naturally linked with the geometric approach to Monge-Ampère operators developed by Lychagin in late 70th. I shall concentrate my attention on the Hitchin generalized complex structure, hyper-Kahler/symplectic and hope to show few interesting examples of its relations with the Monge-Ampère operators and applications.