|
Volume growth and holonomy in nonnegative curvature
Author(s):
Kristopher
Tapp
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3035-3041.
MSC (1991):
Primary 53C20;
Secondary 57S20
Posted:
April 23, 1999
MathSciNet review:
1605945
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
- 1.
- J. Cheeger, Some Examples of Manifolds of Nonnegative Curvature, J. Differential Geom. 8(1972), 623-628. MR 49:6085
- 2.
- J. Cheeger and D. Gromoll, On the structure of compete open manifolds of nonnegative curvature, Ann. of Math. 96 (1972), 413-443. MR 46:8121
- 3.
- J.H. Eschenburg, Comparison theorems and hypersurfaces, Manuscripta Math. 59 (1987), 295-323. MR 89f:53062
- 4.
- L. Guijarro and G. Walschap, The metric projection onto the soul, Trans. Amer. Math. Soc. (to appear). CMP 98:06
- 5.
- S. Kobayashi and K. Nomizu, Foundations of differential geometry I, Interscience Publishers (1963), J. Wiley and Sons. MR 27:2945
- 6.
- G. Perelman, Proof of the soul conjecture of Cheeger and Gromoll, J. Differential Geom. 40(1994), 209-212. MR 95d:53037
- 7.
- V. Schroeder and M. Strake, Volume growth of open manifolds with nonnegative curvature, Ann. Global Anal. Geom., 8, no.2 (1990), 159-165. MR 92e:53052
- 8.
- M. Strake and G. Walschap,
 -flat manifolds and Riemannian submersions, Manuscripta Math., 64(1989), 213-226. MR 90g:53054 - 9.
- J.W. Yim, Space of souls in a complete open manifold of nonnegative curvature, J. Differential Geom. 32 (1990), 429-455. MR 91j:53023
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
53C20,
57S20
Retrieve articles in all Journals with
MSC (1991):
53C20,
57S20
Additional Information:
Kristopher
Tapp
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email:
ktapp@math.upenn.edu
DOI:
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
Posted:
April 23, 1999
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1999,
American Mathematical Society
|
