| 曲面的Gauss方程与Codazzi方程的等价定理 |
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| 引用本文： | 寿淑泓,纪永强.曲面的Gauss方程与Codazzi方程的等价定理[J].湖州师专学报,2011(1):36-41. |
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| 作者姓名： | 寿淑泓 纪永强 |
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| 作者单位： | 湖州师范学院理学院,浙江湖州313000 |
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| 摘 要： | 利用外微分和外积的知识,给出并证明了曲面的Gauss方程在正交标架{r（u,v）;e1（u,v）,e2（u,v）,e3（u,v）}及自然标架{r（u,v）;ru,rv,n}下的二次微分形式的等式与函数的等式的等价定理,以及曲面的Codazzi方程在正交标架及自然标架下的二次微分形式的等式与函数的等式的等价定理.
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| 关 键 词： | Gauss方程 Codazzi方程 等价定理 |
The Equivalent Theorems of Gauss Equations and Codazzi Equations on Surface |
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| Institution: | SHOU Shu - hong , JI Yong - qiang (Faculty of Science, Huzhou Teachers College, Huzhou 313000, China) |
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| Abstract: | Using the knowledge of exterior differential and exterior product,this paper gives and proves the equivalent theorems which are about the equation in quadratic differential form and in function of Gauss equations under orthogonal frame {r（u,v）;e1（u,v）,e2（u,v）,e3（u,v）} or natural frame {r（u,v）;ru,rv,n},and the equivalent theorems which are about the equation in quadratic differential form and in function of Codazzi equations under orthogonal frame or natural frame. |
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| Keywords: | Gauss equations Codazzi equations equivalent theorems |
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