Pincements en courbure de Ricci positive

Erwann Aubry

Pincements en courbure de Ricci positive

Differential Geometry 2007-05-23 v1 Geometric Topology

Authors: Erwann Aubry

Abstract

We show that a complete Riemannian manifold of dimension $n$ with $\Ric\geq n{-}1$ and its $n$ -st eigenvalue close to $n$ is both Gromov-Hausdorff close and diffeomorphic to the standard sphere. This extends, in an optimal way, a result of P. Petersen. We also show that a manifold with $\Ric\geq n{-}1$ and volume close to $\frac{\Vol\sn}{#\pi_1(M)}$ is both Gromov-Hausdorff close and diffeomorphic to the space form $\frac{\sn}{\pi_1(M)}$ . This extends results of T. Colding and T. Yamaguchi.

Keywords

riemannian geometry ricci curvature and riemannian geometry simplicial volume

Cite

@article{arxiv.math/0505408,
  title  = {Pincements en courbure de Ricci positive},
  author = {Erwann Aubry},
  journal= {arXiv preprint arXiv:math/0505408},
  year   = {2007}
}

Comments

To appear in Ann. Sci. Ec. Norm. sup

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