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The Tangent Bundle of an Almost Complex Manifold

Published online by Cambridge University Press:  20 November 2018

László Lempert  and
Róbert Szőke
László Lempert
Affiliation:
Department of Mathematics Purdue University West Lafayette, IN 47907 USA
Róbert Szőke
Affiliation:
Department of Mathematics Purdue University West Lafayette, IN 47907 USA
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Abstract

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Motivated by deformation theory of holomorphic maps between almost complex manifolds we endow, in a natural way, the tangent bundle of an almost complexmanifold with an almost complex structure. We describe various properties of this structure.

Keywords

53C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 1 , 01 March 2001 , pp. 70 - 79
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] de Bartolomeis, P. and Tian, G., Stability of complex vector bundles. J. Differential. Geom. 43 (1996), 231–275.Google Scholar
[2] Gauduchon, P., Appendix: The canonical almost complex structure on the manifold of 1-jets of pseudo-holomorphic mappings between two almost complex manifolds. In: Holomorphic curves in symplectic geometry (eds. M. Audin and J. Lafontaine), Birkhäuser, Boston, 1994, 69–73.Google Scholar
[3] Gromov, M., Pseudo holomorphic curves in symplectic manifolds. Invent. Math. 82 (1985), 307–347.Google Scholar
[4] Kobayashi, S. and Nomizu, K., Foundations of differential geometry. Interscience, New York-London-Sydney, 1969.Google Scholar
[5] McDuff, D. and Salamon, D., J-holomorphic curves and quantum cohomology. University Lecture Series 6, Amer.Math. Soc., Providence, RI, 1994.Google Scholar
[6] Muller, M.-P., Gromov's Schwarz lemma as an estimate of the gradient for holomorphic curves. In: Holomorphic curves in symplectic geometry (eds. M. Audin and J. Lafontaine), Birkhäuser, Boston, 1994, 215–231.Google Scholar
[7] Nijenhuis, A. and Wolf, W., Some integration problems in almost complex and complex manifolds. Ann. of Math. 77 (1963), 424–489.Google Scholar