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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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| Authors: | Ya-jun Yin Ji-ye Wu Ke-zhi Huang Qin-shan Fan |
| Institution: | 1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R. China;Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China 2. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, P. R. China 3. Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China |
| 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. |
| Keywords: | the second gradient operator integral theorem Gaussian curvature Gaussian (or spherical) mapping mapping invariant |
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