Generalized transversely projective structure on a transversely holomorphic foliation
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 automorphi...
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| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120201116X |
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doaj-6ed14c97568247f4a196a051eb2ae02e2020-11-24T22:51:54ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130315116310.1155/S016117120201116XGeneralized transversely projective structure on a transversely holomorphic foliationIndranil Biswas0School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, IndiaThe 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.http://dx.doi.org/10.1155/S016117120201116X |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Indranil Biswas |
| spellingShingle |
Indranil Biswas Generalized transversely projective structure on a transversely holomorphic foliation International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Indranil Biswas |
| author_sort |
Indranil Biswas |
| title |
Generalized transversely projective structure on a
transversely holomorphic foliation |
| title_short |
Generalized transversely projective structure on a
transversely holomorphic foliation |
| title_full |
Generalized transversely projective structure on a
transversely holomorphic foliation |
| title_fullStr |
Generalized transversely projective structure on a
transversely holomorphic foliation |
| title_full_unstemmed |
Generalized transversely projective structure on a
transversely holomorphic foliation |
| title_sort |
generalized transversely projective structure on a
transversely holomorphic foliation |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S016117120201116X |
| work_keys_str_mv |
AT indranilbiswas generalizedtransverselyprojectivestructureonatransverselyholomorphicfoliation |
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