On symplectic classification of effective 3-forms and Monge-Ampere equations

Abstract

We complete the list of normal forms for effective 3-forms with constant coefficients with respect to the natural action of symplectomorphisms in \mathbb{R}^6. We show that the 3-form which corresponds to the Special Lagrangian equation is among the new members of the classification. The symplectic symmetry algebras and their Cartan prolongations for these forms are computed and a local classification theorem for the corresponding Monge-Ampere equations is proved.