Sphere Theorem for Manifolds with Positive Curvature

Bazanfare Mahaman

Sphere Theorem for Manifolds with Positive Curvature

Differential Geometry 2007-05-23 v2

Authors: Bazanfare Mahaman

Abstract

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 $S^{n}.$

Keywords

sphere packings and spherical designs riemannian geometry differential geometry of surfaces and curves in euclidean space

Cite

@article{arxiv.math/0407121,
  title  = {Sphere Theorem for Manifolds with Positive Curvature},
  author = {Bazanfare Mahaman},
  journal= {arXiv preprint arXiv:math/0407121},
  year   = {2007}
}

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