Some recent progress in non-Kahler geometry

被引：9
作者：
Zheng, Fangyang [1 ,2 ]
机构：
[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 11期
关键词：
non-Kahler manifolds; Hermitian geometry; Kahler-like metrics; 53026; 53C55; ORTHOGONAL COMPLEX STRUCTURES; COMPACT; MANIFOLDS; EXISTENCE; METRICS;
D O I：
10.1007/s11425-019-9528-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we discuss some recent progress in the study of non-Kahler manifolds, in particular the Hermitian geometry of flat canonical connections and Kahler-like connections. We also discuss a number of conjectures and open questions in this direction.
引用
收藏
页码：2423 / 2434
页数：12
相关论文
共 39 条
  • [1] Vanishing theorems on Hermitian manifolds
    Alexandrov, B
    Ivanov, S
    [J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2001, 14 (03) : 251 - 265
  • [2] Angella D., COMMUN ANAL GEOM
  • [3] [Anonymous], 2014, ARXIV14042481
  • [4] SELF-DUALITY IN 4-DIMENSIONAL RIEMANNIAN GEOMETRY
    ATIYAH, MF
    HITCHIN, NJ
    SINGER, IM
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1978, 362 (1711): : 425 - 461
  • [5] On the metric structure of non-Kahler complex surfaces
    Belgun, FA
    [J]. MATHEMATISCHE ANNALEN, 2000, 317 (01) : 1 - 40
  • [6] A LOCAL INDEX THEOREM FOR NON KAHLER-MANIFOLDS
    BISMUT, JM
    [J]. MATHEMATISCHE ANNALEN, 1989, 284 (04) : 681 - 699
  • [7] Boothby W. M., 1958, MICH MATH J, V5, P229
  • [8] TWISTOR GEOMETRY AND WARPED PRODUCT ORTHOGONAL COMPLEX STRUCTURES
    Borisov, Lev
    Salamon, Simon
    Viaclovsky, Jeff
    [J]. DUKE MATHEMATICAL JOURNAL, 2011, 156 (01) : 125 - 166
  • [9] A CLASS OF COMPACT, COMPLEX MANIFOLDS WHICH ARE NOT ALGEBRAIC
    CALABI, E
    ECKMANN, B
    [J]. ANNALS OF MATHEMATICS, 1953, 58 (03) : 494 - 500
  • [10] REAL HOMOTOPY THEORY OF KAHLER MANIFOLDS
    DELIGNE, P
    GRIFFITHS, P
    MORGAN, J
    SULLIVAN, D
    [J]. INVENTIONES MATHEMATICAE, 1975, 29 (03) : 245 - 274
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