ON THE TOTAL MEAN CURVATURE OF A NONRIGID SURFACE

被引：4

作者：

Alexandrov, V. A. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2009年 / 50卷 / 05期

关键词：

infinitesimal flex; vector field; flux of a vector field; circulation of a vector field; Green's formula; FORMULA;

D O I：

10.1007/s11202-009-0087-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field, which immediately yields the following well-known theorem: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.

引用

页码：757 / 759

页数：3

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