The aim of this note is to derive a compactness result for complete manifolds whose Ricci curvature is bounded from below. The classical result, usually stated as Bonnet-Myers theorem, provides an estimation of the diameter of a manifold whose Ricci curvature is greater than a strictly positive constant. Weaker assumptions that the Ricci curvature function tends slowly to zero (when the distance from a fixed point goes to infinity) were already considered in [2, 3]. We shall improve here their results.
Cite this article
V. Boju, Louis Funar, A Note on the Bonnet-Myers Theorem. Z. Anal. Anwend. 15 (1996), no. 2, pp. 275–278DOI 10.4171/ZAA/698