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1-COMPLETE SEMIHOLOMORPHIC FOLIATIONS.
- Source :
-
Transactions of the American Mathematical Society . Sep2016, Vol. 368 Issue 9, p6271-6292. 22p. - Publication Year :
- 2016
-
Abstract
- A semiholomorphic foliation of type (n, d) is a differentiable real manifold X of dimension 2n + d, foliated by complex leaves of complex dimension n. In the present work, we introduce an appropriate notion of pseudoconvexity (and consequently, q-completeness) for such spaces, given by the interplay of the usual pseudoconvexity along the leaves, and the positivity of the transversal bundle. For 1-complete real analytic semiholomorphic foliations, we obtain a vanishing theorem for the CR cohomology, which we use to show an extension result for CR functions on Levi flat hypersurfaces and an embedding theorem in CN. In the compact case, we introduce a notion of weak positivity for the transversal bundle, which allows us to construct a real analytic embedding in CPN. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 368
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 113169637
- Full Text :
- https://doi.org/10.1090/tran/6543