Open Access
January 2008 Positively curved cohomogeneity one manifolds and 3-Sasakian geometry
Karsten Grove, Burkhard Wilking, Wolfgang Ziller
J. Differential Geom. 78(1): 33-111 (January 2008). DOI: 10.4310/jdg/1197320603


We provide an exhaustive description of all simply connected positively curved cohomogeneity one manifolds. The description yields a complete classification in all dimensions but 7, where in addition to known examples, our list contains one exceptional space and two infinite families not yet known to carry metrics of positive curvature. The infinite families also carry a 3-Sasakian metric of cohomogeneity one, which is associated to a family of selfdual Einstein orbifold metrics on the 4-sphere constructed by Hitchin.


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Karsten Grove. Burkhard Wilking. Wolfgang Ziller. "Positively curved cohomogeneity one manifolds and 3-Sasakian geometry." J. Differential Geom. 78 (1) 33 - 111, January 2008.


Published: January 2008
First available in Project Euclid: 10 December 2007

zbMATH: 1145.53023
MathSciNet: MR2406265
Digital Object Identifier: 10.4310/jdg/1197320603

Rights: Copyright © 2008 Lehigh University

Vol.78 • No. 1 • January 2008
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