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

作　　者：殷雅俊 吴继业 黄克智 范钦珊 

机构地区：[1]Department of Engineering Mechanics,School of Aerospace,Tsinghua University [2]Division of Mechanics,Nanjing University of Technology,Nanjing 211816,P.R.China [3]Division of Mechanics,Nanjing University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第7期855-862,共8页应用数学和力学（英文版）

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

摘　　要：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 discussedBy 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

关 键 词：the second gradient operator integral theorem Gaussian curvature Gaussian （or spherical） mapping mapping invariant 

分 类 号：O186.1[理学—数学]