Symplectic Geometry of Manifolds with Almost Nowhere Vanishing Closed 2-Form |
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Authors: | Zot'ev D B |
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Institution: | 1. Volgograd State University, Russia
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Abstract: | We study local geometric properties of manifolds equipped with a closed 2-form nondegenerate at all points of a dense proper subset. We introduce the natural notion of tame singular point, at which the matrix of the 2-form degenerates in a regular way. We find a condition for Hamiltonian dynamical systems to be extended smoothly to tame singular points, generalize the Darboux theorem about the local reduction of the matrix of the 2-form to canonical form, and study the singular behavior of directional gradients. |
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