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Mat. Zametki, 2004, Volume 76, Issue 1, Pages 66–77 (Mi mz95)  

This article is cited in 2 scientific papers (total in 2 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.

DOI: https://doi.org/10.4213/mzm95

Full text: PDF file (227 kB)
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English version:
Mathematical Notes, 2004, 76:1, 62–72

Bibliographic databases:

UDC: 514.74
Received: 20.10.2000
Revised: 15.12.2003

Citation: D. B. Zot'ev, “Symplectic Geometry of Manifolds with Almost Nowhere Vanishing Closed 2-Form”, Mat. Zametki, 76:1 (2004), 66–77; Math. Notes, 76:1 (2004), 62–72

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. B. Zot'ev, “Contact degeneracies of closed 2-forms”, Sb. Math., 198:4 (2007), 491–520  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. D. B. Zotev, “Predkvantovanie po Kostantu simplekticheskikh mnogoobrazii s kontaktnymi osobennostyami”, Matem. zametki, 105:6 (2019), 857–878  mathnet  crossref
  • Математические заметки Mathematical Notes
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