| 高斯曲率内蕴公式的几种形式的推导方法 |
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| 引用本文： | 邢家省,高建全,罗秀华.高斯曲率内蕴公式的几种形式的推导方法[J].四川轻化工学院学报,2014(4):82-89. |
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| 作者姓名： | 邢家省 高建全 罗秀华 |
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| 作者单位： | [1]北京航空航天大学数学与系统科学学院,北京100191 [2]数学、信息与行为教育部重点实验室,北京100191 [3]平顶山教育学院数学系,河南平顶山467000 |
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| 基金项目： | 国家自然科学基金项目（11201020） |
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| 摘 要： | 考虑曲面上高斯曲率内蕴公式的表示问题,运用曲面基本方程的矩阵表示法,给出了高斯曲率是内蕴量的直接的显式公式,并指出这种内蕴公式与Brioschi的表示公式是明显一致的;给出了高斯曲率简化公式的推导来源,揭示出了高斯曲率隐式公式的发现过程.
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| 关 键 词： | 曲面的基本方程 曲面结构方程 高斯曲率 内蕴公式 Brioschi公式 |
Derivations with Several forms of Intrinsic Formulas of Gaussian Curvature |
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| XING Jiasheng,GAO Jianquan,LUO Xiuhua.Derivations with Several forms of Intrinsic Formulas of Gaussian Curvature[J].Journal of Sichuan Institute of Light Industry and Chemical Technology,2014(4):82-89. |
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| Authors: | XING Jiasheng GAO Jianquan LUO Xiuhua |
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| Affiliation: | 1. School of Mathematics and Systems Science, Beihang University, Beijing 100191, China; 2. LMIB of the Ministry of Education, Beihang University, Beijing 100191, China ; 3. Department of Mathematics, Pingdingshan Institute of Education, Pingdingshan 467000, China) |
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| Abstract: | The expression of intrinsic formula of Gaussian curvature on curved surface is considered. The direct explicit formula of the intrinsic quantities expressed by Gaussian curvature is derived by means of the matrix expression of curved surface fundamental equation. This intrinsic formula is evidently in accord with Brioschi formula. The derivation of Gaussian curvature simplified formula is demonstrated, which discloses the discovery process of Gaussian curvature implicit formula. |
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| Keywords: | curved surface fundamental equation curved surface constitutive equation Gaussian curvature intrinsic formula Brioschi formula |
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