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The dual foliation in open manifolds with nonnegative sectional curvature
Author(s):
Luis
Guijarro;
Gerard
Walschap
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1419-1425.
MSC (2000):
Primary 53C20
Posted:
December 28, 2007
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Abstract:
We study several properties of the Sharafutdinov dual foliation in open manifolds with nonnegative sectional curvature.
References:
-
- 1.
- Jeff Cheeger and Detlef Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413-443. MR 0309010 (46:8121)
- 2.
- Luis Guijarro, On the metric structure of open manifolds with nonnegative curvature, Pacific J. Math. 196 (2000), no. 2, 429-444. MR 1800586 (2002b:53042)
- 3.
- Luis Guijarro and Gerard Walschap, The metric projection onto the soul, Trans. Amer. Math. Soc. 352 (2000), no. 1, 55-69. MR 1487617 (2000c:53034)
- 4.
- -, Transitive holonomy group and rigidity in nonnegative curvature, Math. Z. 237 (2001), no. 2, 251-257. MR 1838310 (2002j:53055)
- 5.
- G. Perelman, Proof of the soul conjecture of Cheeger and Gromoll, J. Differential Geom. 40 (1994), no. 1, 209-212. MR 1285534 (95d:53037)
- 6.
- Grisha Perelman, Aleksandrov spaces with curvature bounded below II, Unpublished.
- 7.
- V. A. Šarafutdinov, The Pogorelov-Klingenberg theorem for manifolds that are homeomorphic to
, Sibirsk. Mat. Ž. 18 (1977), no. 4, 915-925, 958. MR 0487896 (58:7488) - 8.
- Gerard Walschap, Nonnegatively curved manifolds with souls of codimension
, J. Differential Geom. 27 (1988), no. 3, 525-537. MR 940117 (89g:53067) - 9.
- Burkhard Wilking, A duality theorem for riemannian foliations in nonnegative sectional curvature, Geometric and Functional Analysis (to appear).
- 10.
- Jin-Whan Yim, Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature, Ann. Global Anal. Geom. 6 (1988), no. 2, 191-206. MR 982765 (90a:53049)
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Additional Information:
Luis
Guijarro
Affiliation:
Department of Mathematics, Universidad Autónoma de Madrid, Spain
Email:
luis.guijarro@uam.es
Gerard
Walschap
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma
Email:
gerard@ou.edu
DOI:
10.1090/S0002-9939-07-09047-8
PII:
S 0002-9939(07)09047-8
Keywords:
Wilking dual foliation,
open manifolds with nonnegative sectional curvature
Received by editor(s):
November 29, 2006
Posted:
December 28, 2007
Additional Notes:
The first author was supported by research grant MTM2004-04794-MEC. Most of this work was done during a visit of the second author to Madrid, financed in part by funds of the aforementioned grant.
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2007,
American Mathematical Society
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