Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 3020864
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C44, 53C55

Retrieve articles in all journals with MSC (2010): 53C44, 53C55

Additional Information

Chengjie Yu
Affiliation: Department of Mathematics, Shantou University, Shantou, Guangdong, People’s Republic of China

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.

American Mathematical Society