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Extension of covariant derivative (II): From flat space to curved space

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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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Authors and Affiliations

  1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, 100084, Beijing, China

    Ya-Jun Yin

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  1. Ya-Jun Yin
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Correspondence to Ya-Jun Yin.

Additional information

The project was supported by the NSFC (11072125 and 11272175), the NSF of Jiangsu Province (SBK201140044), and the Specialized Research Fund for Doctoral Program of Higher Education (20130002110044).

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Yin, YJ. Extension of covariant derivative (II): From flat space to curved space. Acta Mech Sin 31, 88–95 (2015). https://doi.org/10.1007/s10409-015-0004-x

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  • DOI: https://doi.org/10.1007/s10409-015-0004-x

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