Sphere Theorem for Manifolds with Positive Curvature

Details Sphere Theorem for Manifolds with Positive Curvature Sphere Theorem for Manifolds with Positive Curvature

2004-07-08

arxiv.org/abs/math/0407121v2

Mathematics

Differential Geometry

Scientific paper

In this paper, we prove that, for any integer $n\ge 2,$ there exists an
$\epsilon_{n} \ge 0$ so that if $M$ is an n-dimensional complete manifold with
sectional curvature $ K_{M}\ge 1$ and if $M$ has conjugate radius bigger than
$\frac{\pi}{2} $ and contains a geodesic loop of length $2(\pi -\epsilon_{n}),$
then $M$ is diffeomorphic to the Euclidian unit sphere $S^{n}.$

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