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L 2 Approaches to Holomorphic Foliations
2015Some results on the L2 \(\bar{\partial }\)-cohomology groups are applied to holomorphic foliations. A basic general result is a nonexistence theorem for the foliation on n-dimensional compact Kahler manifolds whose stable set is a real hypersurface with (n − 2)-convex and pseudoconvex complement. For the special cases such as \(\mathbb{C}\mathbb{P}^{n}\
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Complexifications of transversely holomorphic foliations
Mathematische Annalen, 1985Let \({\mathcal F}\) be a transeversely holomorphic foliation on a paracompact manifold X, of dimension p and complex codimension n. This means that \({\mathcal F}\) is given by an open covering \(\{U_ i\}_{i\in I}\) and local submersions \(f_ i: U_ i\to {\mathbb{C}}^ n\) with fibers of dimension p such that, for i,\(j\in I\), there is a holomorphic ...
Haefliger, A., Sundararaman, D.
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Holomorphic Foliations: Non-singular Case
2021In this chapter we introduce and discuss the concept of holomorphic foliation in the non-singular case. Basic constructions and examples are presented and we also motivate the forthcoming notion of holomorphic foliation with singularities.
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On Transversally Holomorphic Maps of Kählerian Foliations
Acta Applicandae Mathematica, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BARLETTA, Elisabetta, DRAGOMIR, Sorin
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ON BOUNDEDNESS OF FAMILIES OF HOLOMORPHIC FOLIATIONS
International Journal of Mathematics, 2009We get boundedness for certain families of foliations. This is attained after proving a kind of foliated Arakelov inequality.
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Compact Hausdorff Transversally Holomorphic Foliations
1982This is a revised version of part of the lectures given by the author at Trieste Seminar on Complex Analysis and its Applications. The last part of this paper gives a report on the results obtained by Girbau-Haefliger-Sundararaman subsequent to the Seminar. The author would like to thank Professor A. Haefliger for his suggestions. The remaining part of
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