Bonnet-Myers Theorem

The Bonnet-Myers Theorem, also known as Myers's Theorem, is a fundamental result of Riemannian geometry discovered by Sumner Byron Myers in 1941, building on an earlier special case due to Ossian Bonnet. It states that a complete Riemannian manifold whose Ricci curvature is bounded below by a fixed positive constant must be compact, with a diameter no larger than a bound determined by that constant, and consequently must have a finite fundamental group. The theorem is one of the classical global results relating a lower curvature bound to strong topological restrictions on the manifold as a whole.