Odd Type Generalized Complex Structures on 4-Manifolds

被引：1

作者：

Chen, Haojie ^{[1
]}

Nie, Xiaolan ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Generalized complex structure; Transversely holomorphic foliation; Bihermitian structure; 4-manifold;

D O I：

10.1007/s12220-019-00271-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a compact smooth 4-manifold admits generalized complex structures of odd type if and only if it has a transversely holomorphic 2-foliation. We also obtain an equivalent description of generalized complex structures in terms of almost bihermitian structures.

引用

页码：457 / 474

页数：18

共 25 条

[1] [Anonymous], 2004, ARXIVMATHDG0401221
[2] Generalized Kahler manifolds, commuting complex structures, and split tangent bundles
Apostolov, Vestislav
Gualtieri, Marco
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 271 (02) : 561 - 575
[3] Type one generalized Calabi-Yaus
Bailey, Michael
Cavalcanti, Gil R.
Gualtieri, Marco
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2017, 120 : 89 - 95
[4] Symplectic Foliations and Generalized Complex Structures
Bailey, Michael
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2014, 66 (01): : 31 - 56
[5] Bailey M, 2013, J DIFFER GEOM, V95, P1
[6] On transversely holomorphic flows .1.
Brunella, M
[J]. INVENTIONES MATHEMATICAE, 1996, 126 (02) : 265 - 279
[7] Cavalcanti G.R, 2005, ARXIVMATH0501406
[8] Cavalcanti GR, 2007, J DIFFER GEOM, V76, P35
[9] Blow-up of generalized complex 4-manifolds
Cavalcanti, Gil R.
Gualtieri, Marco
[J]. JOURNAL OF TOPOLOGY, 2009, 2 (04) : 840 - 864
[10] The Monge-Ampere equation for non-integrable almost complex structures
Chu, Jianchun
Tosatti, Valentino
Weinkove, Ben
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2019, 21 (07) : 1949 - 1984

← 1 2 3 →