Metric tangent spaces to Euclidean spaces

被引：0
|
作者：
Dordovski D.V. [1 ]
机构：
[1] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Donetsk 83114, 74, R. Luxemburg Str.
来源：
Journal of Mathematical Sciences | 2011年 / 179卷 / 2期
关键词：
Euclidean spaces; isometries of an Euclidean space; Metric pretangent spaces;
D O I：
10.1007/s10958-011-0591-4
中图分类号：
学科分类号：
摘要：
We prove that the metric spaces pretangent to a finite-dimensional Euclidean or unitary space E are isometric to E. As a consequence of this result, we describe the metric pretangent spaces at the nonsingular points of smooth surfaces. It is also proved that there exist the spaces pretangent to the Hilbert space l2, which are not isometric to it. © 2011 Springer Science+Business Media, Inc.
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页码：229 / 244
页数：15
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