Let be a smooth foliation with complex leaves and let be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space . In particular we concentrate on the following two themes: function theory for the algebra and cohomology with values in .
Sia una varietà differenziabile fogliata con foglie complesse e sia il fascio dei germi delle funzioni differenziabili su , olomorfe lungo le foglie. Si studia lo spazio anellato ; in particolare la teoria delle funzioni per l'algebra e la coomologia a valori in .
@article{RLIN_1993_9_4_2_115_0, author = {Giuliana Gigante and Giuseppe Tomassini}, title = {Foliations with complex leaves}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni}, volume = {4}, year = {1993}, pages = {115-120}, zbl = {0784.32027}, mrnumber = {1233399}, language = {en}, url = {http://dml.mathdoc.fr/item/RLIN_1993_9_4_2_115_0} }
Gigante, Giuliana; Tomassini, Giuseppe. Foliations with complex leaves. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993) pp. 115-120. http://gdmltest.u-ga.fr/item/RLIN_1993_9_4_2_115_0/
[1] Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. France, 90, 1962, 193-259. | MR 150342 | Zbl 0106.05501
- ,[2] Analytic Convexity. Ann. Scuola Norm. Sup. Pisa, 7, 1980, 287-372. | MR 581145 | Zbl 0435.35039
- ,[3] Noyaux pour résoudre l'équation dans des classes ultradifférentiables sur des compacts irréguliers de . Preprint.
- ,[4] Local complex foliations of real submanifolds. Math. Ann., 209, 1970, 1-30. | MR 346185 | Zbl 0267.32006
,[5] Tangential Cauchy-Riemann equations and uniform approximation. Pacific J. Math., 33, N. 1, 1970, 101-108. | MR 264117 | Zbl 0184.31103
,[6] Division et extension dans l'algèbre d'un ouvert pseudo-convex à bord lisse de . Math. Z., 189, 1985, 421-447. | MR 783566 | Zbl 0547.32009
- ,[7] | MR 1045639 | Zbl 0271.32001
, An Introduction to Complex Analysis in Several Variables. North-Holland1973.[8] Intrinsic distances, measures and geometric function theory. Bull. Am. Math. Soc., 82, 1976, 357-416. | MR 414940 | Zbl 0346.32031
,[9] Global regularity for on weakly pseudoconvex manifolds. Trans. Amer. Math. Soc., 181, 1973, 273-292. | MR 344703 | Zbl 0276.35071
,[10] A Proof of the Malgrange Preparation Theorem. Proceedings of Liverpool Singularities, I. Lecture notes in mathematics, 192, Springer-Verlag, New York1971, 97-105. | MR 412460 | Zbl 0212.10702
,[11] Levi flat submanifolds and biholomorphic extension of foliations. Ann. Scuola Norm. Sup. Pisa, 26, 1972, 664-681. | MR 425158 | Zbl 0272.57013
,[12] 100, 1981. | MR 627768 | Zbl 0476.32033
, A class of hyperbolic manifolds. Recent developments in several complex variables. Ann. of Math. Stud., Princeton Univ. Press, N.[13] Komplexe analytische Blätterung reeler Mannigfaltigkeiten in . Math. Ann., 136, 1958, 111-133. | MR 101924 | Zbl 0092.29902
,[14] Extension d'objects CR. Math. Z., 194, 1987, 471-486. | MR 881705 | Zbl 0629.32015
,