Myers's theorem

Myers's theorem is a result in Riemannian geometry, which concerns the relationship between the geometry of a complete Riemannian manifold and its topology. Specifically, the theorem states that if \( M \) is a complete Riemannian manifold that has non-negative Ricci curvature, then \( M \) can be isometrically embedded into a Euclidean space of a certain dimension.