Foliations with vanishing Chern classes



In this paper we aim at the description of foliations having tangent sheaf T F with c 1 (T F) = c 2(T F) = 0 on non-uniruled projective manifolds. We prove that the universal covering of the ambient manifold splits as a product, and that the Zariski closure of a general leaf of F is an Abelian variety. It turns out that the analytic type of the Zariski closures of leaves may vary from leaf to leaf. We discuss how this variation is related to arithmetic properties of the tangent sheaf of the foliation.


foliation Chern class transverse structure 

Mathematical subject classification

32S65 37F75 57R30 


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Copyright information

© Sociedade Brasileira de Matemática 2013

Authors and Affiliations

  1. 1.IMPAHorto, Rio de JaneiroBrazil
  2. 2.IRMARRennes CedexFrance

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