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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  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
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