K-结构变换下的非线性Cauchy-Riemann方程

On the Nonlinear Cauchy-Riemann Equation of K-Structural Transformation

引入了复域上关于复函数的K-结构变换,讨论了K-结构变换下的非线性Cauchy-Riemann方程,得到了关于Cauchy-Riemann方程的推广均为K-结构变换的不同形式的结论 ,特别是各推广方程的系数只与K结构函数的分量及其一阶偏导数有关。

The K-structural transformation of complex functions in complex domain is introduced.The nonlinear Cauchy-Riemann equation under K-structure transformation is discussed.It is concluded that the generalization of Cauchy-Riemann equation is in different forms of K-structure transformation.Especially,the coefficients of the generalized equations are only related to the components of K-structure functions and their first-order partial derivatives.