Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
نویسندگان
چکیده
Let M n be a complete Riemannian manifold of bounded curvature, say IKI ~ 1. Given a small number, e > 0, we put M n = SWn(e) u ~n(e), where SW n (e) consists of those points at which the injectivity radius of the exponential map is ~ e. The complementary set, ~n (e) is called the e-collapsed part of Mn. If x E SWn(e) , r ~ e, then the metric ball BJr) is quasi-isometric, with small distortion, to the flat ball Bo(r) in the Euclidean space, Rn • After slightly
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