MathSciDoc: An Archive for Mathematician ∫

 
Log In
Sign Up
Help
Go
 

Scalar curvature on compact complex manifolds

Xiaokui Yang Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China; HCMS, CEMS, NCNIS, HLM, UCAS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

Differential Geometry mathscidoc:2207.10001

Transactions of the American Mathematical Society, 371, (3), 2073-2087, 2019.2
In this paper, we prove that, a compact complex manifold $X$ admits a smooth Hermitian metric with positive (resp., negative) scalar curvature if and only if $K_X$ (resp., $K_X^{-1}$) is not pseudo-effective. On the contrary, we also show that on an arbitrary compact complex manifold $X$ with complex dimension $\geq 2$, there exist smooth Hermitian metrics with positive total scalar curvature, and one of the key ingredients in the proof relies on a recent solution to the Gauduchon conjecture by G. Székelyhidi, V. Tosatti, and B. Weinkove.
No keywords uploaded!
[ Download ] [ 2022-07-03 15:20:40 uploaded by yangxk ] [ 301 downloads ] [ 0 comments ] 
@inproceedings{xiaokui2019scalar,
  title={Scalar curvature on compact complex manifolds},
  author={Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703152040545845524},
  booktitle={Transactions of the American Mathematical Society},
  volume={371},
  number={3},
  pages={2073-2087},
  year={2019},
}
Xiaokui Yang. Scalar curvature on compact complex manifolds. 2019. Vol. 371. In Transactions of the American Mathematical Society. pp.2073-2087. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703152040545845524.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved