International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 151-163
doi:10.1155/S016117120201116X
Generalized transversely projective structure on a
transversely holomorphic foliation
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Received 29 November 2000; Revised 4 June 2001
Copyright © 2002 Indranil Biswas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The results of Biswas (2000) are extended to the situation of
transversely projective foliations. In particular, it is shown
that a transversely holomorphic foliation defined using everywhere
locally nondegenerate maps to a projective space
ℂℙn, and whose transition functions are given
by automorphisms of the projective space, has a canonical
transversely projective structure. Such a foliation is also
associated with a transversely holomorphic section of N⊗−k
for each k∈[3,n+1], where N is the normal bundle to
the foliation. These transversely holomorphic sections are also
flat with respect to the Bott partial connection.