| Myers Theorem |
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| CATEGORIES ABOUT MYERS THEOREM | |
| riemannian geometry | |
| mathematical theorems | |
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It states that if Ricci Curvature of a Complete Riemannian manifold ''M'' is bounded below by , then its diameter is at most . Moreover, if the diameter is equal to , then the manifold is Isometric to a sphere of a constant Sectional Curvature ''k''. This result also holds for the Universal Cover of such a Riemannian manifold, in particular both ''M'' and its cover are compact, so the cover is finite-sheeted and ''M'' has finite Fundamental Group . REFERENCES S. B. Myers, ''Riemannian manifolds with positive mean curvature,'' Duke Mathematical Journal Volume 8, Number 2 (1941), 401-404 M. P. do Carmo, ''Riemannian Geometry,'' Birkhäuser, Boston, Mass.(1992) |
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