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July  2009, 25(2): 537-544. doi: 10.3934/dcds.2009.25.537

Holomorphic foliations transverse to manifolds with corners

Toshikazu Ito 1, and  Bruno Scárdua 2,

1. 

Department of Natural Science - Ryukoku University, Fushimi-Ku, Kyoto 612, Japan
2. 

Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21.945-970, Rio de Janeiro, RJ

Received  June 2008 Revised  December 2008 Published  June 2009

We study the geometrical and dynamical properties of a holomorphic vector field on a complex surface, assumed to be transverse to the boundary of a domain which is a non-smooth manifold with boundary and corners. We obtain hyperbolicity and prove a compact leaf result. For a pseudoconvex domain with boundary diffeomorphic to the boundary of a bidisc in $\mathbb C^2$ the foliation is pull-back of a liner hyperbolic foliation. If moreover the diffeomorphism is transversely holomorphic then we have linearization.
Keywords: Holomorphic foliation, manifold with corners, hyperbolic holonomy..
Mathematics Subject Classification: Primary: 37F75; Secondary: 32M25, 32S6.
Citation: Toshikazu Ito, Bruno Scárdua. Holomorphic foliations transverse to manifolds with corners. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 537-544. doi: 10.3934/dcds.2009.25.537
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