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Myers theorem - Definition and Overview |
| Related Words: Assertion, Assumption, Axiom, Basis, Brocard, Conjecture, Data, Deduction, Dictum, Formula, Foundation, Fundamental, Ground, Hypothesis, Law, Lemma |
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Myers theorem is a classical theorem in Riemannian geometry.
It states that if Ricci curvature of a complete Riemannian manifold is bounded below by <math>\left(n-1\right)k > 0 \,\!<math>, then its diameter is at most <math>\pi/\sqrt{k}<math>,
in particular any such manifold is compact and it has finite fundamental group.
Moreover, if the diameter is equal to <math>\pi/\sqrt{k}<math>, then the manifold is isometric to a sphere of a constant sectional curvature k.
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