Foliations with complex leaves

Giuliana Gigante; Giuseppe Tomassini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 2, page 115-120
  • ISSN: 1120-6330

Abstract

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Let X be a smooth foliation with complex leaves and let D be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space X , D . In particular we concentrate on the following two themes: function theory for the algebra D ⁢ X and cohomology with values in D .

How to cite

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Gigante, Giuliana, and Tomassini, Giuseppe. "Foliations with complex leaves." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.2 (1993): 115-120. <http://eudml.org/doc/244170>.

@article{Gigante1993,
abstract = {Let \( X \) be a smooth foliation with complex leaves and let \( \mathcal\{D\} \) be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space \( (X, \mathcal\{D\}) \). In particular we concentrate on the following two themes: function theory for the algebra \( \mathcal\{D\}(X) \) and cohomology with values in \( \mathcal\{D\} \).},
author = {Gigante, Giuliana, Tomassini, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Foliations; Several complex variables and analytic spaces; CR-structures; smooth foliation; complex leaves; cohomology; Kobayashi metric},
language = {eng},
month = {6},
number = {2},
pages = {115-120},
publisher = {Accademia Nazionale dei Lincei},
title = {Foliations with complex leaves},
url = {http://eudml.org/doc/244170},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Gigante, Giuliana
AU - Tomassini, Giuseppe
TI - Foliations with complex leaves
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/6//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 2
SP - 115
EP - 120
AB - Let \( X \) be a smooth foliation with complex leaves and let \( \mathcal{D} \) be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space \( (X, \mathcal{D}) \). In particular we concentrate on the following two themes: function theory for the algebra \( \mathcal{D}(X) \) and cohomology with values in \( \mathcal{D} \).
LA - eng
KW - Foliations; Several complex variables and analytic spaces; CR-structures; smooth foliation; complex leaves; cohomology; Kobayashi metric
UR - http://eudml.org/doc/244170
ER -

References

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  1. ANDREOTTI, A. - GRAUERT, H., Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. France, 90, 1962, 193-259. Zbl0106.05501MR150342
  2. ANDREOTTI, A. - NACINOVICH, M., Analytic Convexity. Ann. Scuola Norm. Sup. Pisa, 7, 1980, 287-372. Zbl0435.35039MR581145
  3. CHAUMAT, J. - CHOLLET, A. M., Noyaux pour résoudre l'équation ∂ ¯ dans des classes ultradifférentiables sur des compacts irréguliers de C n . Preprint. 
  4. FREEMAN, M., Local complex foliations of real submanifolds. Math. Ann., 209, 1970, 1-30. Zbl0267.32006MR346185
  5. FREEMAN, M., Tangential Cauchy-Riemann equations and uniform approximation. Pacific J. Math., 33, N. 1, 1970, 101-108. Zbl0184.31103MR264117
  6. GAY, R. - SEBBAR, A., Division et extension dans l'algèbre A ∞ ⁢ Ω d'un ouvert pseudo-convex à bord lisse de C n . Math. Z., 189, 1985, 421-447. Zbl0547.32009MR783566DOI10.1007/BF01164163
  7. HÖRMANDER, L., An Introduction to Complex Analysis in Several Variables. North-Holland1973. Zbl0271.32001MR1045639
  8. KOBAYASHI, S., Intrinsic distances, measures and geometric function theory. Bull. Am. Math. Soc., 82, 1976, 357-416. Zbl0346.32031MR414940
  9. KOHN, J. J., Global regularity for ∂ ¯ on weakly pseudoconvex manifolds. Trans. Amer. Math. Soc., 181, 1973, 273-292. Zbl0276.35071MR344703
  10. NIRENBERG, L., A Proof of the Malgrange Preparation Theorem. Proceedings of Liverpool Singularities, I. Lecture notes in mathematics, 192, Springer-Verlag, New York1971, 97-105. Zbl0212.10702MR412460
  11. REA, C., Levi flat submanifolds and biholomorphic extension of foliations. Ann. Scuola Norm. Sup. Pisa, 26, 1972, 664-681. Zbl0272.57013MR425158
  12. SIBONY, N., A class of hyperbolic manifolds. Recent developments in several complex variables. Ann. of Math. Stud., Princeton Univ. Press, N. 100, 1981. Zbl0476.32033MR627768
  13. SOMMER, F., Komplexe analytische Blätterung reeler Mannigfaltigkeiten in C n . Math. Ann., 136, 1958, 111-133. Zbl0092.29902MR101924
  14. TOMASSINI, G., Extension d'objects CR. Math. Z., 194, 1987, 471-486. Zbl0629.32015MR881705DOI10.1007/BF01161916

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