Actions of discrete groups on nonpositively curved spaces.
Bernhard Leeb, Michael Kapovich (1996)
Mathematische Annalen
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Bernhard Leeb, Michael Kapovich (1996)
Mathematische Annalen
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M. Anderson (1992)
Geometric and functional analysis
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Frédéric Paulin (1988)
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J. Cheeger, X. Rong (1996)
Geometric and functional analysis
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J.-H. Eschenburg (1982)
Inventiones mathematicae
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Ruberman, Daniel (2001)
Geometry & Topology
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Takao Yamaguchi (1985)
Mathematische Zeitschrift
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Grove, Karsten, Ziller, Wolfgang (2000)
Annals of Mathematics. Second Series
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M. Gromov, W. Thurston (1987)
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Meintrup, David, Schick, Thomas (2002)
The New York Journal of Mathematics [electronic only]
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M.T. Anderson, J. Cheeger (1991)
Geometric and functional analysis
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Karsten Grove, Luigi Verdiani, Burkhard Wilking, Wolfgang Ziller (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case when both are equal to two, where existence of non-negatively curved metrics is known.