Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Real analytic structures on a symplectic manifold

Authors: Frank Kutzschebauch and Frank Loose
Journal: Proc. Amer. Math. Soc. 128 (2000), 3009-3016
MSC (1991): Primary 53C15; Secondary 32C05
Published electronically: April 28, 2000
MathSciNet review: 1769452
Full-text PDF

Abstract | References | Similar Articles | Additional Information


We prove that every symplectic manifold possesses a real analytic structure. Moreover this structure is unique up to isomorphism.

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

  • [1] Grauert, H., On Levi's problem and the imbedding of real-analytic manifolds. Ann. of Math. 68 (1958), 460-472 MR 20:5299
  • [2] Grauert, H. and R. Remmert, Theory of Stein spaces. Springer-Verlag, Berlin Heidelberg New York 1979 MR 82d:32001
  • [3] Guillemin, V. and S. Sternberg, Symplectic techniques in physics. Cambridge University Press, Cambridge 1990 MR 91d:58073
  • [4] Hirsch, M., Differential topology. Springer-Verlag, Berlin Heidelberg New York 1988 MR 96c:57001
  • [5] Illman, S., Every proper smooth action of a Lie group is equivalent to a real analytic action, a contribution to Hilbert's fifth problem. Ann. of Math. Stud. 138 (1995), 189-220 MR 97a:57037
  • [6] Illman, S. and S. Kankaarinta, Some basic results for real analytic proper $G$-manifolds. Preprint Helsinki 1998
  • [7] Kutzschebauch, F., On the uniqueness of the analyticity of a proper $G$-action. Manuscripta Math. 90 (1996), 17-22 MR 97k:57047
  • [8] ---, Eigentliche Wirkungen von Lie-Gruppen auf reell-analytischen Mannigfaltigkeiten. Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik, Ruhr- Universität Bochum, Heft 5 (1994)
  • [9] Matumoto, T. and M. Shiota, Unique triangulation of the orbit space of a differentiable transformation group and its applications, homotopy theory and related topics. Adv. Stud. Pure Math. 9 (1986), 41-55 MR 88g:57041
  • [10] Mihalache, N., Special neighborhoods of subsets in complex spaces. Math. Z. 221 (1996), 49-58 MR 96j:32006
  • [11] Moser, J., On the volume element of a manifold. Trans. Am. Math. Soc. 120 (1965), 286-294 MR 32:409
  • [12] Narasimhan, R., Analysis on real and complex manifolds. North-Holland Publishing Company, Amsterdam 1973 MR 49:11576
  • [13] Schoen, R. and S.T. Yau, Lectures on differential geometry. International Press, Boston 1994 MR 97d:53001
  • [14] Whitney, H., Analytic extensions of differentiable functions defined in closed sets. Trans. Am. Math. Soc. 30 (1934), 63-89 CMP 95:18
  • [15] ---, Differentiable manifolds. Ann. of Math. 37 (1936), 645-680
  • [16] Whitney, H. and F. Bruhat, Quelques proprietés fondamentales des ensembles analytiques. Comment. Math. Helv. 33 (1959), 132-160 MR 21:889

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C15, 32C05

Retrieve articles in all journals with MSC (1991): 53C15, 32C05

Additional Information

Frank Kutzschebauch
Affiliation: Mathematisches Institut der Universität, Rheinsprung 21, CH – 4051 Basel, Switzerland
Address at time of publication: Matematiska Institutionen, Box 480, S-751 06 Uppsala, Sweden

Frank Loose
Affiliation: Mathematisches Institut der Universität, Auf der Morgenstelle 10, D – 72076 Tübingen, Germany

Received by editor(s): December 9, 1998
Published electronically: April 28, 2000
Additional Notes: The first author was partially supported by SNF (Schweizerische Nationalfonds)
Communicated by: Leslie Saper
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society