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September 2012 On positive quaternionic Kähler manifolds with $b_{4} = 1$
Jin Hong Kim, Hee Kwon Lee
Osaka J. Math. 49(3): 551-562 (September 2012).


Let $M$ be a positive quaternionic Kähler manifold of dimension $4m$. In earlier papers, Fang and the first author showed that if the symmetry rank is greater than or equal to $[m/2]+3$, then $M$ is isometric to $\mathbf{HP}^{m}$ or $\mathit{Gr}_{2}(\mathbf{C}^{m+2})$. The goal of this paper is to give a more refined classification result for positive quaternionic Kähler manifolds (in particular, of relatively low dimension or with even $m$) whose fourth Betti number equals one. To be precise, we show in this paper that if the symmetry rank of $M$ with $b_{4}(M)=1$ is no less than $[m/2]+2$ for $m \ge 5$, then $M$ is isometric to $\mathbf{HP}^{m}$.


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Jin Hong Kim. Hee Kwon Lee. "On positive quaternionic Kähler manifolds with $b_{4} = 1$." Osaka J. Math. 49 (3) 551 - 562, September 2012.


Published: September 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1268.53059
MathSciNet: MR2993057

Primary: 53C26

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics


Vol.49 • No. 3 • September 2012
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