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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Wu-Zheng's splitting conjecture


Author: Chengjie Yu
Journal: Proc. Amer. Math. Soc. 141 (2013), 1791-1793
MSC (2010): Primary 53C44; Secondary 53C55
Published electronically: October 25, 2012
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11570-9
PII: S 0002-9939(2012)11570-9
Keywords: Kähler manifolds, bisectional curvature, splitting theorem
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.