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

 

An example of compact Kähler manifold with nonnegative quadratic bisectional curvature


Authors: Qun Li, Damin Wu and Fangyang Zheng
Journal: Proc. Amer. Math. Soc. 141 (2013), 2117-2126
MSC (2010): Primary 32M10, 53C55; Secondary 53C21, 53C30
Published electronically: February 12, 2013
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Abstract: We construct a compact Kähler manifold of nonnegative quadratic bisectional curvature which does not admit any Kähler metric of nonnegative orthogonal bisectional curvature. The manifold is a 7-dimensional Kähler $ C$-space with second Betti number equal to 1, and its canonical metric is a Kähler-Einstein metric of positive scalar curvature.


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Additional Information

Qun Li
Affiliation: Department of Mathematics and Statistics, Wright State University, 3640 Colonel Glenn Highway, Dayton, Ohio 45435
Email: qun.li@wright.edu

Damin Wu
Affiliation: Department of Mathematics, The Ohio State University, 1179 University Drive, Newark, Ohio 43055
Address at time of publication: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: dwu@math.ohio-state.edu, damin.wu@uconn.edu

Fangyang Zheng
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210 – and – Center for Mathematical Sciences, Zhejiang University, Hangzhou, 310027 People’s Republic of China
Email: zheng@math.ohio-state.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11596-0
PII: S 0002-9939(2013)11596-0
Received by editor(s): October 7, 2011
Published electronically: February 12, 2013
Communicated by: Lei Ni
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.