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.
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K. Diederich and A. Sukhov, Plurisubharmonic functions and almost complex Stein structures, (preprint), ArXiv math/0603417v1, to appearMich. Math. J.
J. Duval, Un théorème de Green presque complexe,Ann. Inst. Fourier (Grenoble) 54 (2004), 2357–2367.
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.
D. McDuff and D. Salamon,J-Holomorphic Curves and Quantum Cohomolgy, University Lectures Series 6, American Mathematical Society, Providence, RI, 1994.
D. McDuff and D. Salamon,J-Holomorphic Curves and Symplectic Topology, American Mathematical Society, Colloquium Publications 52, Providence, RI, 2004.
B. Malgrange,Lectures on the theory of functions of several complex variables. Notes by Raghavan Narasimhan, Tata Institute of Fundamental Research, Bombay, 1958.
R. Narasimhan,Analysis on Real and Complex Manifolds, Advanced Studies in Pure Mathematics1, NorthHolland Publishing Co., AmsterdamLondon, American Elsevier Publishing Co. New York, 1973.
A. Nijenhuis and W.B. Woolf, Some integration problems in almostcomplex and complex manifolds,Ann. of Math. 77 (1963), 424–489.
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.
A. Sukhov and A. Tumanov, Filling hypersurfaces by discs in almost complex manifolds of dimension 2,Indiana Univ. Math. J. 57 (2008), 509–544.
A. Sukhov and A. Tumanov, Filling real hypersurfaces by pseudoholomorphic discs,J. Geom. Anal. 18 (2008), 632–649.
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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
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DOI: https://doi.org/10.1007/BF03191215