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.

Mongodi, S., Tomassini, G. (2016). 1-complete semiholomorphic foliations. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368(9), 6271-6292 [10.1090/tran/6543].

1-complete semiholomorphic foliations

Mongodi S.
;
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.
Articolo in rivista - Articolo scientifico
Complex spaces; CR geometry; Semiholomorphic foliations;
English
9-dic-2015
2016
368
9
6271
6292
open
Mongodi, S., Tomassini, G. (2016). 1-complete semiholomorphic foliations. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368(9), 6271-6292 [10.1090/tran/6543].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/349844
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