| Extension of covariant derivative(Ⅱ): From flat space to curved space |
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| 作者姓名： | Ya-Jun Yin |
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| 作者单位： | Department of Engineering Mechanics,School of Aerospace, Tsinghua University |
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| 基金项目： | supported by the NSFC(11072125 and 11272175);the NSF of Jiangsu Province(SBK201140044);the Specialized Research Fund for Doctoral Program of Higher Education(20130002110044) |
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| 摘 要： | This paper extends the classical covariant derivative to the generalized covariant derivative on curved surfaces. The basement for the extension is similar to the previous paper, i.e., the axiom of the covariant form invariability. Based on the generalized covariant derivative, a covariant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analysis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.
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| 关 键 词： | Tensor analysis on curved surfaces · Classical covariant derivative and generalized covariant derivative · Axiom of the covarian |
Extension of covariant derivative (II): From flat space to curved space |
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| Ya-Jun Yin.Extension of covariant derivative (II): From flat space to curved space[J].Acta Mechanica Sinica,2015,31(1):88-95. |
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| Authors: | Ya-Jun Yin |
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| Institution: | 1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, 100084, Beijing, China
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| Abstract: | This paper extends the classical covariant derivative to the generalized covariant derivative on curved surfaces. The basement for the extension is similar to the previous paper, i.e., the axiom of the covariant form invariability. Based on the generalized covariant derivative, a covariant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analysis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces. |
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