Nonexistence of Levi flat hypersurfaces with positive normal bundle in compact Kahler manifolds of dimension ≥ 3

被引：1

作者：

Biard, Severine ^{[1
,3
]}

Iordan, Andrei ^{[2
]}

机构：

[1] Univ Paris 06, Inst Math, UMR 7586, CNRS, Case 247,4 Pl Jussieu, F-75252 Paris 05, France

[2] Sorbonne Univ, Fac Sci & Ingn, Inst Math Jussieu Paris Rive Gauche, 4 Pl Jussieu, F-75252 Paris 05, France

[3] Univ Polytech Hauts de France, LAMAV, Campus Mt Houy, F-59313 Valenciennes 9, France

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2020年 / 31卷 / 01期

关键词：

Levi flat hypersurface; weighted partial derivative-equation; MINIMAL SETS; SPACES; REGULARITY; FOLIATIONS; OPERATOR; THEOREM;

D O I：

10.1142/S0129167X20500044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a compact connected Milder manifold of dimension >= 3 and L a C-infinity Levi flat hypersurface in X. Then the normal bundle to the Levi foliation does not admit a Hermitian metric with positive curvature along the leaves. This represents an answer to a conjecture of Marco Brunella.

引用

页数：14

共 33 条

[1]

Andreotti A., 1961, Ann. Scuola Norm. Sup. Pisa Cl. Sci., V15, P283

[2]

Andreotti A., 1965, PUBL MATH-PARIS, V25, P81

[3]

[Anonymous], 1967, J. Math. Soc. Jpn, DOI DOI 10.1215/KJM/1250524335

[4]

Aronszajn Aro57 N., 1957, J. Math. Pures Appl., V36, P235

[5]