Complex nilmanifolds with constant holomorphic sectional curvature
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- by Yulu Li and Fangyang Zheng PDF
- Proc. Amer. Math. Soc. 150 (2022), 319-326 Request permission
Abstract:
A well known conjecture in complex geometry states that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler if the constant is non-zero and must be Chern flat if the constant is zero. The conjecture is confirmed in complex dimension $2$, by the work of Balas-Gauduchon [Math. Z. 189 (1985), pp. 193–210]. (when the constant is zero or negative) and by Apostolov-Davidov-Muskarov [Trans. Amer. Math. Soc. 348 (1996), pp. 3051–3063] (when the constant is positive). For higher dimensions, the conjecture is still largely unknown. In this article, we restrict ourselves to the class of complex nilmanifolds and confirm the conjecture in that case.References
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Additional Information
- Yulu Li
- Affiliation: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People’s Republic of China
- Email: 1320779072@qq.com
- Fangyang Zheng
- Affiliation: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People’s Republic of China
- MR Author ID: 272367
- Email: 20190045@cqnu.edu.cn
- Received by editor(s): March 21, 2021
- Published electronically: October 12, 2021
- Additional Notes: The research was partially supported by NSFC grant # 12071050 and Chongqing Normal University
The second author is the corresponding author - Communicated by: Jia-Ping Wang
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 319-326
- MSC (2020): Primary 53C55; Secondary 53C05
- DOI: https://doi.org/10.1090/proc/15724
- MathSciNet review: 4335879