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International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 151-163
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 n, 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 Nk 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.