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Moser stability for locally conformally symplectic structures


Authors: G. Bande and D. Kotschick
Journal: Proc. Amer. Math. Soc. 137 (2009), 2419-2424
MSC (2000): Primary 53D99; Secondary 57R17, 58H15
DOI: https://doi.org/10.1090/S0002-9939-09-09821-9
Published electronically: January 28, 2009
MathSciNet review: 2495277
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Abstract: We formulate and prove the analogue of Moser's stability theorem for locally conformally symplectic structures. As special cases we recover some results previously proved by Banyaga.


References [Enhancements On Off] (What's this?)

  • 1. A. Banyaga, Some properties of locally conformal symplectic structures, Comment. Math. Helv. 77 (2002), no. 2, 383-398. MR 1915047 (2003d:53134)
  • 2. A. Banyaga, Examples of non $ d_\omega$-exact locally conformal symplectic forms, J. Geom. 87 (2007), 1-13. MR 2372512 (2008i:53113)
  • 3. S. Dragomir and L. Ornea, Locally conformal Kähler geometry, Progress in Mathematics 155, Birkhäuser Boston, Inc., Boston, MA, 1998. MR 1481969 (99a:53081)
  • 4. F. Guédira and A. Lichnerowicz, Géométrie des algèbres de Lie locales de Kirillov, J. Math. Pures Appl. 63 (1984), no. 4, 407-484. MR 789560 (86j:58045)
  • 5. S. Haller and T. Rybicki, On the group of diffeomorphisms preserving a locally conformal symplectic structure, Ann. Global Anal. Geom. 17 (1999), no. 5, 475-502. MR 1715157 (2001f:53164)
  • 6. H. C. Lee, A kind of even-dimensional differential geometry and its application to exterior calculus, Amer. J. of Math. 65 (1943), 433-438. MR 0008495 (5:15h)
  • 7. J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. MR 0182927 (32:409)
  • 8. I. Vaisman, Locally conformal symplectic manifolds, Internat. J. Math. Math. Sci. 8 (1985), no. 3, 521-536. MR 809073 (87d:53076)
  • 9. F. W. Warner, Foundations of differentiable manifolds and Lie groups, Scott, Foresman and Co., Glenview, IL, and London, 1971. MR 0295244 (45:4312)

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Additional Information

G. Bande
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy
Email: gbande@unica.it

D. Kotschick
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresien- str. 39, 80333 München, Germany
Email: dieter@member.ams.org

DOI: https://doi.org/10.1090/S0002-9939-09-09821-9
Received by editor(s): October 8, 2008
Published electronically: January 28, 2009
Additional Notes: This work was carried out while the second author was a Visiting Professor at the Università degli Studi di Cagliari, supported by the Regione Autonoma della Sardegna
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2009 G. Bande and D. Kotschick

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