Lifting group actions and nonnegative curvature

Grove, Karsten; Ziller, Wolfgang

doi:10.1090/S0002-9947-2011-05272-4

Lifting group actions and nonnegative curvature
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Trans. Amer. Math. Soc. 363 (2011), 2865-2890 Request permission

Abstract:

We examine the question when a group acting by cohomogeneity one on the base of a principal $\operatorname {G}$-bundle can be lifted to the total space and commutes with the action by $\operatorname {G}$. We answer this question completely when the base of the principle bundle is $4$-dimensional.

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