| 从第二类梯度算子和第二类积分定理到Gauss（球面）映射不变量 |
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| 引用本文： | 殷雅俊,吴继业,黄克智,范钦珊.从第二类梯度算子和第二类积分定理到Gauss（球面）映射不变量[J].应用数学和力学,2008,29(7):775-782. |
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| 作者姓名： | 殷雅俊 吴继业 黄克智 范钦珊 |
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| 作者单位： | 1.清华大学 航天航空学院 工程力学系,北京 100084; |
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| 摘 要： | 将第二类梯度算子、第二类积分定理、Gauss曲率相关的积分定理和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．
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| 关 键 词： | 第二类梯度算子 第二类积分定理 Gauss曲率 Gauss（球面）映射 不变量 |
| 收稿时间： | 2007-11-20 |
From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants |
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| YIN Ya-jun,WU Ji-ye,HUANG Ke-zhi,FAN Qin-shan.From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants[J].Applied Mathematics and Mechanics,2008,29(7):775-782. |
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| Authors: | YIN Ya-jun WU Ji-ye HUANG Ke-zhi FAN Qin-shan |
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| Institution: | 1.Department of Engineering Mechanics, School of Aerospace, FML, Tsinghua University, Beijing 100084, P. R. China;Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China |
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| Abstract: | Through the combination of the second gradient operator,the second category of integral theorems,the Gauss-curvature-based integral theorems and the Gauss(or spherical) mapping,a series of invariants or geometric conservation quantities under Gauss(or spherical) mapping were revealed.From these mapping invariants important transfor mations between original curved surface and the spherical surface were derived.The potential applications of these invariants and transformations to geometryare prospected. |
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