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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Volume growth and holonomy
in nonnegative curvature


Author: Kristopher Tapp
Journal: Proc. Amer. Math. Soc. 127 (1999), 3035-3041
MSC (1991): Primary 53C20; Secondary 57S20
Published electronically: April 23, 1999
MathSciNet review: 1605945
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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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Additional Information

Kristopher Tapp
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email: ktapp@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04893-5
PII: S 0002-9939(99)04893-5
Keywords: Volume growth, holonomy, nonnegative curvature, soul
Received by editor(s): December 11, 1997
Published electronically: April 23, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society