Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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Grisha Perelman, Aleksandrov spaces with curvature bounded below II, Unpublished.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 $ {\bf R}\sp{n}$, Sibirsk. Mat. Ž. 18 (1977), no. 4, 915-925, 958. MR 0487896 (58:7488)

8.
Gerard Walschap, Nonnegatively curved manifolds with souls of codimension $ 2$, 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)


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C20

Retrieve articles in all Journals with MSC (2000): 53C20


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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google