Physics Daily - Physics Encyclopedia and Research Articles
      Back to Physics Daily Main Menu Go to Index of Topics/Articles

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 \left(n-1\right)k > 0 \,\!, then its diameter is at most \pi/\sqrt{k}, in particular any such manifold is compact and it has finite fundamental group.

Moreover, if the diameter is equal to \pi/\sqrt{k}, then the manifold is isometric to a sphere of a constant sectional curvature k.

07-10-2008 09:35:13
The contents of this article are licensed from Wikipedia.org under the GNU Free Documentation License. How to see transparent copy
 
PhysicsDaily.com Legal info