Hermitian metrics of positive holomorphic sectional curvature on fibrations

被引：0
作者：
Ananya Chaturvedi
Gordon Heier
机构：
[1] Tata Institute of Fundamental Research,Department of Mathematics
[2] University of Houston,Department of Mathematics
来源：
Mathematische Zeitschrift | 2020年 / 295卷
关键词：
Compact complex manifolds; Hermitian metrics; Fibrations; Positive holomorphic sectional curvature; 14D06; 32L05; 32Q10; 53C55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use of a warped product metric as in the work by Cheung in case of negative holomorphic sectional curvature, but differs in certain key aspects, e.g., in that it does not use the subadditivity property for holomorphic sectional curvature due to Grauert-Reckziegel and Wu.
引用
收藏
页码：349 / 364
页数：15
相关论文
共 38 条
  • [1] Alvarez A(2015)Optimal pinching for the holomorphic sectional curvature of Hitchin’s metrics on Hirzebruch surfaces Contemp. Math. 654 133-142
  • [2] Chaturvedi A(2018)On projectivized vector bundles and positive holomorphic sectional curvature Proc. Am. Math. Soc. 146 2877-2882
  • [3] Heier G(1969)Manifolds of negative curvature Trans. Am. Math. Soc. 145 1-49
  • [4] Alvarez A(1989)Hermitian metrics of negative holomorphic sectional curvature on some hyperbolic manifolds Math. Z. 201 105-119
  • [5] Heier G(1973)Families of negatively curved Hermitian manifolds Proc. Am. Math. Soc. 39 362-366
  • [6] Zheng F(2019)Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle J. Differ. Geom. 111 303-314
  • [7] Bishop R(2003)Families of rationally connected varieties J. Am. Math. Soc. 16 57-67
  • [8] O’Neill B(1965)Hermitesche metriken und normale familien holomorpher abbildungen Math. Z. 89 108-125
  • [9] Cheung C-K(2010)On the canonical line bundle and negative holomorphic sectional curvature Math. Res. Lett. 17 1101-1110
  • [10] Cowen M(2016)Kähler manifolds of semi-negative holomorphic sectional curvature J. Differ. Geom. 104 419-441
1234