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Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (7): 855-862 .doi: https://doi.org/10.1007/s10483-008-0703-1

• Articles • 上一篇    下一篇

从第二类梯度算子和第二类积分定理得到Gauss（球面）映射不变量

殷雅俊1,2,吴继业1,黄克智1,范钦珊2   

  1. 1.清华大学航天航空学院力学系，北京 100084；
    2.南京工业大学力学部，南京 211816
  • 收稿日期:2007-11-20 修回日期:2008-06-12 出版日期:2008-07-03 发布日期:2008-01-01
  • 通讯作者: 殷雅俊

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

YIN Ya-jun1,2,WU Ji-ye1,HUANG Ke-zhi1, FAN Qin-shan2   

  1. 1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R. China;
    2. Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China
  • Received:2007-11-20 Revised:2008-06-12 Online:2008-07-03 Published:2008-01-01
  • Contact: YIN Ya-jun

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摘要： 将第二类梯度算子、第二类积分定理、Gauss曲率有关的积分定理和Gauss（球面）映射相结合，证明了一系列Gauss（球面）映射不变量。从这些不变量中，得到一系列从原始曲面到（Gauss单位）球面的变换。这些不变量和变换，在几何学、物理学、生物力学和力学中，都有潜在的用途。

关键词: Gauss曲率, 第二类梯度算子, 不变量, 第二类积分定理, Gauss（球面）映射

Abstract: By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation
quantities under Gaussian (or spherical) mapping are revealed. From
these mapping invariants important transformations between original
curved surface and the spherical surface are derived. The potential
applications of these invariants and transformations to geometry are
discussed.

Key words: the second gradient operator, integral theorem,Gaussian curvature, Gaussian (or spherical) mapping, mapping invariant

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