Geodesic
SPHERE THEOREM FOR MANIFOLDS WITH POSITIVE CURVATURE
Glasgow mathematical journal, Tome 48 (2006) no. 1, pp. 37-40

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DOI

In this paper, we prove that, for any integer $n\ge 2,$ and any $\delta > 0$ there exists an $\epsilon(n,\delta) \ge 0$ such that if $M$ is an $n$-dimensional complete manifold with sectional curvature $K_M \ge 1$ and if $M$ has conjugate radius $\rho \ge\frac{\pi}{2}+\delta $ and contains a geodesic loop of length $2(\pi-\epsilon(n,\delta))$ then $M$ is diffeomorphic to the Euclidian unit sphere $\mathbb{S}^{n}.$
DOI : 10.1017/S0017089505002843
Mots-clés : 53C20, 53C21 
MAHAMAN, BAZANFARÉ. SPHERE THEOREM FOR MANIFOLDS WITH POSITIVE CURVATURE. Glasgow mathematical journal, Tome 48 (2006) no. 1, pp. 37-40. doi: 10.1017/S0017089505002843
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     journal = {Glasgow mathematical journal},
     pages = {37--40},
     year = {2006},
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     doi = {10.1017/S0017089505002843},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002843/}
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