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Myers theorem
Myers theorem is a classical theorem in Riemannian geometry.
It states that if Ricci curvature of a complete Riemannian manifold is bounded below by 
, then its diameter is at most 
,
in particular any such manifold is compact and it has finite fundamental group.
Moreover, if the diameter is equal to , then the manifold is isometric to a sphere of a constant sectional curvature k.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details