从第二类梯度算子和第二类积分定理到Gauss(球面)映射不变量

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

将第二类梯度算子、第二类积分定理、Gauss曲率相关的积分定理和Gauss(球面)映射相结合,证明了一系列Gauss(球面)映射不变量.从这些不变量中,得到一系列从原始曲面到(Gauss单位)球面的变换.这些不变量和变换,在几何学、物理学、生物力学和力学中,都有潜在的用途.

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 transformations between original curved surface and the spherical surface were derived. The potential applications of these invariants and transformations to geometry are prospected.