A classification of Monge-Ampère equations

V. V. Lychagin; V. N. Rubtsov; I. V. Chekalov

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Liouville forms in a neighborhood of an isotropic embedding

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A Liouville form on a symplectic manifold $(X, ω)$ is by definition a potential $β$ of the symplectic form $- d β = ω$ . Its center $M$ is given by $β^{- 1} (0)$ . A normal form for certain Liouville forms in a neighborhood of its center is given.

Special connections on symplectic manifolds

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The reduction of symplectic structure and Sternberg construction

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Invariant properties of the generalized canonical mappings

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One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.

Applications of convex integration to symplectic and contact geometry

Dusa McDuff (1987)

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We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures