Kähler manifolds with split tangent bundle

Marco Brunella; Jorge Vitório Pereira; Frédéric Touzet

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 2, page 241-252
  • ISSN: 0037-9484

Abstract

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This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.

How to cite

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Brunella, Marco, Vitório Pereira, Jorge, and Touzet, Frédéric. "Kähler manifolds with split tangent bundle." Bulletin de la Société Mathématique de France 134.2 (2006): 241-252. <http://eudml.org/doc/272499>.

@article{Brunella2006,
abstract = {This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.},
author = {Brunella, Marco, Vitório Pereira, Jorge, Touzet, Frédéric},
journal = {Bulletin de la Société Mathématique de France},
keywords = {kähler manifolds; holomorphic foliations; uniformisation; integrability},
language = {eng},
number = {2},
pages = {241-252},
publisher = {Société mathématique de France},
title = {Kähler manifolds with split tangent bundle},
url = {http://eudml.org/doc/272499},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Brunella, Marco
AU - Vitório Pereira, Jorge
AU - Touzet, Frédéric
TI - Kähler manifolds with split tangent bundle
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 2
SP - 241
EP - 252
AB - This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.
LA - eng
KW - kähler manifolds; holomorphic foliations; uniformisation; integrability
UR - http://eudml.org/doc/272499
ER -

References

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  2. [2] A. Beauville – « Complex manifolds with split tangent bundle », Complex analysis and algebraic geometry, de Gruyter, Berlin, 2000, p. 61–70. Zbl1001.32010MR1760872
  3. [3] F. Bogomolov & M. McQuillan – « Rational curves on foliated varieties », Preprint IHÉS (2001). 
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  6. [6] —, « Some remarks on parabolic foliations », Contemp. Math.389 (2005), p. 91–102. Zbl1140.32309MR2181959
  7. [7] F. Campana & T. Peternell – « Projective manifolds with splitting tangent bundle I », Math. Z.241 (2002), p. 613–637. Zbl1065.14054MR1938707
  8. [8] J.-P. Demailly – « On the frobenius integrability of certain holomorphic p -forms », Complex geometry (Göttingen, 2000), Springer, Berlin, 2002, p. 93–98. Zbl1011.32019MR1922099
  9. [9] S. Druel – « Variétés algébriques dont le fibré tangent est totalement décomposé », J. reine angew. Math. 522 (2000), p. 9161–171. Zbl0946.14005MR1758581
  10. [10] C. Godbillon – « Feuilletages : études géométriques », Progress in Mathematics, vol. 98, Birkhäuser Verlag, Basel, 1991. Zbl0724.58002MR1120547
  11. [11] J. V. Pereira – « Global stability for holomorphic foliations on Kaehler manifolds », Qual. Theory Dyn. Syst.2 (2001), p. 381–384. Zbl1074.53019MR1913291
  12. [12] —, « Fibrations, divisors and transcendental leaves », J. Algebraic Geom. 15 (2006), no. 1, p. 87–110. Zbl1089.32027MR2177196
  13. [13] C. Simpson – « Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization », J. Amer. Math. Soc.1 (1988), p. 867–918. Zbl0669.58008MR944577

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