Nilpotent structures and invariant metrics on collapsed manifolds
نویسندگان
چکیده
منابع مشابه
Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
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,...
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O. I n t r o d u c t i o n We will begin by briefly recall ing the not ion of F-s t ruc tu re and some relevant related concepts; for fur ther details, see [CG1], [CG2], [CR] and sections 1 3 below. An F-structure, .f, on a manifold, M n, is a kind of general ized torus action. Specifically, it is a sheaf of Lie algebras, together wi th a homomorphism of this sheaf onto a sheaf of abel ian Lie ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1992
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-1992-1126118-x