Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature
- 109 Downloads
We construct a distance nonincreasing deformation retraction from a complete open manifold of nonnegative sectional curvature to a soul. Using this retraction, we prove that any two souls are isometric and also obtain a lower bound on the injectivity radius of such manifolds.
KeywordsGroup Theory Sectional Curvature Injectivity Radius Open Manifold Nonnegative Sectional Curvature
Unable to display preview. Download preview PDF.
- P. Buser and H. Karcher: Gromov's almost flat manifolds, Société mathématique de France (1981).Google Scholar
- J. Cheeger and D. Ebin: Comparison theorems in Riemannian geometry, North-Holland Publishing Co. (1975).Google Scholar
- J. Cheeger and D. Gromoll. On the structure of complete manifolds of nonnegative curvature, Ann. Math. 96 (1972), 413–443.Google Scholar
- V. A. Sharafutdinov: The radius of injectivity of a complete open manifold of nonnegative curvature (Russian), Dokl. Akad. Nauk SSSR 231 (1976), 46–48.Google Scholar
- V. A. Sharafutdinov: The Pogorelov-Klingenberg Theorem for manifolds homeomorphic to R n (Russian), Sib. Mat. Zh. 18 (1977) 4, 915–925.Google Scholar
- V. A. Sharafutdinov: Convex sets in a manifold of non-negative curvature (Russian), Mat. Zap. 26 (1979) 1, 129–136.Google Scholar