Skip to main content
Log in

Notes on the Diederich-Sukhov-Tumanov normalization for almost complex structures

  • Published:
Collectanea mathematica Aims and scope Submit manuscript

Abstract

In this paper, written for non specialists, we discuss several points in the elementary theory of almost complex manifolds, with a focus on the question of choice of special coordinates and on the obstruction given by the Nijenhuis tensor.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Diederich and A. Sukhov, Plurisubharmonic functions and almost complex Stein structures, (preprint), ArXiv math/0603417v1, to appearMich. Math. J.

  2. J. Duval, Un théorème de Green presque complexe,Ann. Inst. Fourier (Grenoble) 54 (2004), 2357–2367.

    MATH  MathSciNet  Google Scholar 

  3. S. Ivashkovich and J.-P. Rosay, Schwarztype lemmas for solutions of\(\bar \partial - inequalities\) and complete hyperbolicity of almost complex manifolds,Ann. Inst. Fourier (Grenoble) 54 (2004), 2387–2435.

    MATH  MathSciNet  Google Scholar 

  4. D. McDuff and D. Salamon,J-Holomorphic Curves and Quantum Cohomolgy, University Lectures Series 6, American Mathematical Society, Providence, RI, 1994.

    Google Scholar 

  5. D. McDuff and D. Salamon,J-Holomorphic Curves and Symplectic Topology, American Mathematical Society, Colloquium Publications 52, Providence, RI, 2004.

  6. B. Malgrange,Lectures on the theory of functions of several complex variables. Notes by Raghavan Narasimhan, Tata Institute of Fundamental Research, Bombay, 1958.

    Google Scholar 

  7. R. Narasimhan,Analysis on Real and Complex Manifolds, Advanced Studies in Pure Mathematics1, NorthHolland Publishing Co., AmsterdamLondon, American Elsevier Publishing Co. New York, 1973.

    Google Scholar 

  8. A. Nijenhuis and W.B. Woolf, Some integration problems in almostcomplex and complex manifolds,Ann. of Math. 77 (1963), 424–489.

    Article  MathSciNet  Google Scholar 

  9. J.-C. Sikorav, Some properties of holomorphic curves in almost complex maniflds,Holomorphic Curves in Symplectic Geometry, 165–189, Progr. Math., 117, Birkhäuser, Basel, 1994.

    Google Scholar 

  10. A. Sukhov and A. Tumanov, Filling hypersurfaces by discs in almost complex manifolds of dimension 2,Indiana Univ. Math. J. 57 (2008), 509–544.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Sukhov and A. Tumanov, Filling real hypersurfaces by pseudoholomorphic discs,J. Geom. Anal. 18 (2008), 632–649.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean-Pierre Rosay.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rosay, JP. Notes on the Diederich-Sukhov-Tumanov normalization for almost complex structures. Collect. Math. 60, 43–62 (2009). https://doi.org/10.1007/BF03191215

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03191215

Keywords

MSC2000

Navigation