Volume growth and holonomy in nonnegative curvature

Tapp, Kristopher

doi:10.1090/S0002-9939-99-04893-5

Volume growth and holonomy in nonnegative curvature
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Proc. Amer. Math. Soc. 127 (1999), 3035-3041 Request permission

Abstract:

The volume growth of an open manifold of nonnegative sectional curvature is proven to be bounded above by the difference between the codimension of the soul and the maximal dimension of an orbit of the action of the normal holonomy group of the soul. Additionally, an example of a simply-connected soul with a non-compact normal holonomy group is constructed.

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