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On holomorphic foliations in complex surfaces transverse to a sphere

On holomorphic foliations in complex surfaces transverse to a sphere We prove that a holomorphic foliation Ϝ on a Stein surface transverse to the boundary of a 4-ball is conjugated inside the ball to the foliation generated by the holomorphic vector field $$z\frac{\partial }{{\partial z}} + (z + w)\frac{\partial }{{\partial w}}$$ , provided that the transversely holomorphic flow induced by Ϝ on the boundary of the ball has a parabolic closed orbit. The proof contains a classification of transversely holomorphic flows on 3-manifolds with a parabolic closed orbit. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

On holomorphic foliations in complex surfaces transverse to a sphere

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 1995 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/BF01236988
Publisher site
See Article on Publisher Site

Abstract

We prove that a holomorphic foliation Ϝ on a Stein surface transverse to the boundary of a 4-ball is conjugated inside the ball to the foliation generated by the holomorphic vector field $$z\frac{\partial }{{\partial z}} + (z + w)\frac{\partial }{{\partial w}}$$ , provided that the transversely holomorphic flow induced by Ϝ on the boundary of the ball has a parabolic closed orbit. The proof contains a classification of transversely holomorphic flows on 3-manifolds with a parabolic closed orbit.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Feb 12, 2005

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