Nilpotent structures and invariant metrics on collapsed manifolds
Nilpotent structures and invariant metrics on collapsed manifolds
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DOI：
10.1090/s0894-0347-1992-1126118-x
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发表时间：
1992-05
影响因子：
3.9
通讯作者：
J. Cheeger;K. Fukaya;M. Gromov
中科院分区：
文献类型：
--
作者：
J. Cheeger;K. Fukaya;M. Gromov
设Mn是一个有界曲率的完备黎曼流形，设Iki 0，我们设Mn=Wn(C)UFn(C)，其中？1n(E)由指数映射的内射半径为>；e的点组成.补集&“n(C)称为Mn的e-折叠部分.如果xE4(N)，r<；E，则度量球Bx(R)对欧氏空间Rn中的平坦球B0(R)是拟等距的，且变形很小.
Let Mn be a complete Riemannian manifold of bounded curvature, say IKI 0, we put Mn = W n(c) U Fn (c), where ?1n (e) consists of those points at which the injectivity radius of the exponential map is > e. The complementary set, &"n (c) is called the e-collapsed part of Mn. If x E 4 (n), r < E, then the metric ball Bx (r) is quasi-isometric, with small distortion, to the flat ball B0(r) in the Euclidean space, Rn . After slightly