Isometric folding of Riemannian manifolds
Isometric folding of Riemannian manifolds
复制标题
黎曼流形的等距折叠
DOI：
10.1017/s0308210500019788
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
S. A. Robertson
中科院分区：
文献类型：
--
作者：
S. A. Robertson
概要当一张纸在手中被揉皱，然后在桌面上压扁时，由此形成的折痕图案受到某些简单规则的控制。这些规则推广到关于将黎曼流形等距折叠成彼此的定理。最有趣的结果适用于域和上域具有相同维数的情况。主要的技术证明相结合的概念量与霍普夫的概念程度的地图。
Synopsis When a sheet of paper is crumpled in the hands and then crushed flat against a desk-top, the pattern of creases so formed is governed by certain simple rules. These rules generalize to theorems on folding Riemannian manifolds isometrically into one another. The most interesting results apply to the case in which domain and codomain have the same dimension. The main technique of proof combines the notion of volume with Hopf's concept of the degree of a map.