From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants

YIN Ya-jun; WU Ji-ye; HUANG Ke-zhi; FAN Qin-shan

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(7): 775-782

YIN Ya-jun, WU Ji-ye, HUANG Ke-zhi, FAN Qin-shan. From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants[J]. Applied Mathematics and Mechanics, 2008, 29(7): 775-782.

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From the Second Gradient Operator and Second Category of Integral Theorems to Gauss or Spherical Mapping Invariants

1.
Department of Engineering Mechanics, School of Aerospace, FML, Tsinghua University, Beijing 100084, P. R. China;
Division of Mechanics, Nanjing University of Technology, Nanjing 211816, P. R. China

Received Date: 2007-11-20
Rev Recd Date: 2008-06-12
Publish Date: 2008-07-15

Abstract

Abstract

Through the combination of the second gradient operator,the second category of integral theorems,the Gauss-curvature-based integral theorems and the Gauss(or spherical) mapping,a series of invariants or geometric conservation quantities under Gauss(or spherical) mapping were revealed.From these mapping invariants important transfor mations between original curved surface and the spherical surface were derived.The potential applications of these invariants and transformations to geometryare prospected.
- second gradient operator,
- integral the orem,
- Gauss curvature,
- Gauss(or spherical) mapping,
- mapping invariants

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References(9)

References

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