Theorem of Bonnet-Schoenberg-Myers
The theorem of Bonnet-Schoenberg-Myers is a well-known theorem of the Géométrie riemannienne. It shows how local constraints on metric a riemannienne impose total conditions on the geometry of the variety. Its demonstration rests on a traditional use of the Formule of the second variation.
The case of equality was studied:
Under the preceding notations, if the diameter of is equal to , then is isometric with the Euclidean Sphère of ray .
The theorem of Meyer has the following well-known corollary:
the fundamental group of riemannienne a compact variety of positive curve is a finished group.
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