This article is cited in 4 papers

Symplectic Geometry of Manifolds with Almost Nowhere Vanishing Closed 2-Form

D. B. Zot'ev

Volgograd State Technical University

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.

UDC: 514.74

Received: 20.10.2000
Revised: 15.12.2003

DOI: 10.4213/mzm95

 English version: Mathematical Notes, 2004, 76:1, 62–72

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