Nonnegatively curved Alexandrov spaces with souls of codimension two
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Abstract:
In this paper, we study a complete noncompact nonnegatively curved Alexandrov space $A$ with a soul $S$ of codimension two. We establish some structural results under additional regularity assumptions. As an application, we conclude that in this case Sharafutdinov retraction, $\pi :\ A\to S$, is a submetry.References
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Additional Information
- Xueping Li
- Affiliation: Department of Mathematics, Capital Normal University, Beijing, People’s Republic of China
- Email: xuepingli@jsnu.edu.cn
- Received by editor(s): December 31, 2012
- Published electronically: February 3, 2015
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 3901-3928
- MSC (2010): Primary 53C20, 53C99; Secondary 57N65
- DOI: https://doi.org/10.1090/S0002-9947-2015-06149-2
- MathSciNet review: 3324914