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Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (7): 855-862 .doi: https://doi.org/10.1007/s10483-008-0703-1

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

YIN Ya-jun1,2,WU Ji-ye1,HUANG Ke-zhi1, FAN Qin-shan2   

  1. 1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R. China;
    2. Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China
  • Received:2007-11-20 Revised:2008-06-12 Online:2008-07-03 Published:2008-01-01
  • Contact: YIN Ya-jun

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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.

Key words: the second gradient operator, integral theorem,Gaussian curvature, Gaussian (or spherical) mapping, mapping invariant

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