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From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

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Abstract

By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation quantities under Gaussian (or spherical) mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed.

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Authors and Affiliations

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

    Ya-jun Yin  (殷雅俊), Ji-ye Wu  (吴继业) & Ke-zhi Huang  (黄克智)

  2. Division of Mechanics, Nanjing University of Technology, Nanjing, 211816, P. R. China

    Ya-jun Yin  (殷雅俊) & Qin-shan Fan  (范钦珊)

Authors
  1. Ya-jun Yin  (殷雅俊)
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  2. Ji-ye Wu  (吴继业)
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  3. Ke-zhi Huang  (黄克智)
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  4. Qin-shan Fan  (范钦珊)
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Corresponding author

Correspondence to Ya-jun Yin  (殷雅俊).

Additional information

Communicated by GUO Xing-ming

Project supported by the National Natural Science Foundation of China (No. 10572076)

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Yin, Yj., Wu, Jy., Huang, Kz. et al. From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants. Appl. Math. Mech.-Engl. Ed. 29, 855–862 (2008). https://doi.org/10.1007/s10483-008-0703-1

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  • DOI: https://doi.org/10.1007/s10483-008-0703-1

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Chinese Library Classification

2000 Mathematics Subject Classification

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