Conjugate Radius and Sphere Theorem
Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 214-220
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Bessa [Be] proved that for given $n$ and ${{i}_{0}}$ , there exists an $\varepsilon (\text{n,}\,{{i}_{0}})\,>\,0$ depending on $n$ , ${{i}_{0}}$ such that if $M$ admits a metric $g$ satisfying $\text{Ri}{{\text{c}}_{(M,g)}}\ge n-1,\text{in}{{\text{j}}_{(M,g)}}\ge {{i}_{0}}\,>\,0$ and $\text{dia}{{\text{m}}_{(M,g)}}\,\ge \,\pi \,-\,\varepsilon $ , then $M$ is diffeomorphic to the standard sphere. In this note, we improve this result by replacing a lower bound on the injectivity radius with a lower bound of the conjugate radius.
Paeng, Seong-Hun; Yun, Jong-Gug. Conjugate Radius and Sphere Theorem. Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 214-220. doi: 10.4153/CMB-1999-026-6
@article{10_4153_CMB_1999_026_6,
author = {Paeng, Seong-Hun and Yun, Jong-Gug},
title = {Conjugate {Radius} and {Sphere} {Theorem}},
journal = {Canadian mathematical bulletin},
pages = {214--220},
year = {1999},
volume = {42},
number = {2},
doi = {10.4153/CMB-1999-026-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-026-6/}
}
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