Open Access
June 2014 Rotational symmetry of Ricci solitons in higher dimensions
Simon Brendle
J. Differential Geom. 97(2): 191-214 (June 2014). DOI: 10.4310/jdg/1405447804


Let $(M, g)$ be a steady gradient Ricci soliton of dimension $n \geq 4$ which has positive sectional curvature and is asymptotically cylindrical. Under these assumptions, we show that $(M, g)$ is rotationally symmetric. In particular, our results apply to steady gradient Ricci solitons in dimension $4$ which are $\kappa$-noncollapsed and have positive isotropic curvature.


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Simon Brendle. "Rotational symmetry of Ricci solitons in higher dimensions." J. Differential Geom. 97 (2) 191 - 214, June 2014.


Published: June 2014
First available in Project Euclid: 15 July 2014

zbMATH: 1305.53072
MathSciNet: MR3231974
Digital Object Identifier: 10.4310/jdg/1405447804

Rights: Copyright © 2014 Lehigh University

Vol.97 • No. 2 • June 2014
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