A note on Wu-Zheng’s splitting conjecture
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- by Chengjie Yu PDF
- Proc. Amer. Math. Soc. 141 (2013), 1791-1793 Request permission
Abstract:
Cao’s splitting theorem says that for any complete Kähler-Ricci flow $(M,g(t))$ with $t\in [0,T)$, $M$ simply connected and nonnegative bounded holomorphic bisectional curvature, $(M,g(t))$ is holomorphically isometric to $\mathbb {C}^k\times (N,h(t))$, where $(N,h(t))$ is a Kähler-Ricci flow with positive Ricci curvature for $t>0$. In this article, we show that $k=n-r$, where $r$ is the Ricci rank of the initial metric. As a corollary, we also confirm a splitting conjecture of Wu and Zheng when curvature is assumed to be bounded.References
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Additional Information
- Chengjie Yu
- Affiliation: Department of Mathematics, Shantou University, Shantou, Guangdong, People’s Republic of China
- Email: cjyu@stu.edu.cn
- Received by editor(s): September 3, 2011
- Published electronically: October 25, 2012
- Additional Notes: The author’s research was partially supported by the National Natural Science Foundation of China (11001161) and (10901072).
- Communicated by: Lei Ni
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1791-1793
- MSC (2010): Primary 53C44; Secondary 53C55
- DOI: https://doi.org/10.1090/S0002-9939-2012-11570-9
- MathSciNet review: 3020864