The dual foliation in open manifolds with nonnegative sectional curvature
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- by Luis Guijarro and Gerard Walschap
- Proc. Amer. Math. Soc. 136 (2008), 1419-1425
- DOI: https://doi.org/10.1090/S0002-9939-07-09047-8
- Published electronically: 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
- Jeff Cheeger and Detlef Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443. MR 309010, DOI 10.2307/1970819
- Luis Guijarro, On the metric structure of open manifolds with nonnegative curvature, Pacific J. Math. 196 (2000), no. 2, 429–444. MR 1800586, DOI 10.2140/pjm.2000.196.429
- Luis Guijarro and Gerard Walschap, The metric projection onto the soul, Trans. Amer. Math. Soc. 352 (2000), no. 1, 55–69. MR 1487617, DOI 10.1090/S0002-9947-99-02237-0
- Luis Guijarro and Gerard Walschap, Transitive holonomy group and rigidity in nonnegative curvature, Math. Z. 237 (2001), no. 2, 251–257. MR 1838310, DOI 10.1007/PL00004867
- G. Perelman, Proof of the soul conjecture of Cheeger and Gromoll, J. Differential Geom. 40 (1994), no. 1, 209–212. MR 1285534
- Grisha Perelman, Aleksandrov spaces with curvature bounded below II, Unpublished.
- V. A. Šarafutdinov, The Pogorelov-Klingenberg theorem for manifolds that are homeomorphic to $\textbf {R}^{n}$, Sibirsk. Mat. Ž. 18 (1977), no. 4, 915–925, 958 (Russian). MR 0487896
- Gerard Walschap, Nonnegatively curved manifolds with souls of codimension $2$, J. Differential Geom. 27 (1988), no. 3, 525–537. MR 940117
- Burkhard Wilking, A duality theorem for riemannian foliations in nonnegative sectional curvature, Geometric and Functional Analysis (to appear).
- 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, DOI 10.1007/BF00133039
Bibliographic Information
- Luis Guijarro
- Affiliation: Department of Mathematics, Universidad Autónoma de Madrid, Spain
- MR Author ID: 363262
- Email: luis.guijarro@uam.es
- Gerard Walschap
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma
- Email: gerard@ou.edu
- Received by editor(s): November 29, 2006
- Published electronically: 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 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 1419-1425
- MSC (2000): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-07-09047-8
- MathSciNet review: 2367115