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ON EXISTENCE AND QUASICONFORMAL DEFORMATIONS OF TRANSVERSELY HOLOMORPHIC FOLIATIONS
 

Summary: ON EXISTENCE AND QUASICONFORMAL DEFORMATIONS
OF TRANSVERSELY HOLOMORPHIC FOLIATIONS
Taro Asuke
B­=u B@O:
Department of Mathematics
Kyoto University
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February 27, 2004
Abstract. We review our recent work on transversely holomorphic foliations of
complex codimension one. Some remarks from a viewpoint of characteristic classes
are also given.
There are many sources of transversely holomorphic foliations, e.g., holomorphic
vector elds, group actions, etc. They are of their own interest even simply viewed
as foliations of real codimension two [5]. It seems however diĘcult to construct
examples. It is also diĘcult to tell if a given foliation of real codimension two admits
a transverse holomorphic structure. As an attempt to answer these problems, we
considered transversely quasiconformal foliations in [3]. A foliation is said to be
transversely quasiconformal if there is a real number K for which the holonomy
pseudogroup consists of K-quasiconformal local homeomorphisms. If a foliation is
K-quasiconformal, any in nitesimal circle on the normal bundle will be deformed

  

Source: Asuke, Taro - Graduate School of Mathematical Sciences, University of Tokyo

 

Collections: Mathematics