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

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

1.
清华大学航天航空学院工程力学系,北京 100084;
南京工业大学力学部,南京 211816

基金项目: 国家自然科学基金资助项目(10572076)

详细信息

作者简介:
殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:jinyj@mail.tsinghua.edu.cn).

中图分类号: O186.1
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出版历程
- 收稿日期: 2007-11-20
- 修回日期: 2008-06-12
- 刊出日期: 2008-07-15

From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants

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

摘要

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．
- 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
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.
- second gradient operator /
- integral the orem /
- Gauss curvature /
- Gauss(or spherical) mapping /
- mapping invariants

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参考文献(9)

[1]	Baumgart T, Hess S T, Webb W. Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension[J].Nature,2003,425(6960):821-824. doi: 10.1038/nature02013
[2]	YIN Ya-jun, CHEN Yan-qiu, NI Dong,et al.Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell membranes[J].J Biomechanics,2005,38(7):1433-1440. doi: 10.1016/j.jbiomech.2004.06.024
[3]	Yin Y, Yin J, Ni D. General mathematical frame for open or closed biomembranes: equilibrium theory and geometrically constraint equation[J].Journal of Mathematical Biology,2005,51(4):403-413. doi: 10.1007/s00285-005-0330-x
[4]	Yin Y, Yin J, Lv C. Equilibrium theory in 2D Riemann manifold for heterogeneous biomembranes with arbitrary variational modes[J].Journal of Geometry and Physics,2008,58(1):122-132. doi: 10.1016/j.geomphys.2007.10.001
[5]	YIN Ya-jun. Integral theorems based on a new gradient operator derived from biomembranes (Part Ⅰ): Fundamentals[J].Tsinghua Science and Technology,2005,10(3):372-375. doi: 10.1016/S1007-0214(05)70083-3
[6]	YIN Ya-jun. Integral theorems based on a new gradient operator derived from biomembranes (Part Ⅱ): Applications[J].Tsinghua Science and Technology,2005,10(3):376-380. doi: 10.1016/S1007-0214(05)70084-5
[7]	Yin Y, YIN Jie, WU Ji-ye.The second gradient operator and integral theorems for tensor fields on curved surfaces[J].Applied Mathematical Sciences,2007,1(30):1465-1484.
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[9]	黄克智，薛明德，陆明万.张量分析(第二版)[M].北京：清华大学出版社,2003.

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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

作者简介:
殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:jinyj@mail.tsinghua.edu.cn).

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From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants

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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

作者简介: 殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:jinyj@mail.tsinghua.edu.cn).

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出版历程

From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants

计量

出版历程

目录

作者简介:
殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:jinyj@mail.tsinghua.edu.cn).