Abstract:

Analytic functions are the important research area in complex variable functions. It is not extensive because the real and imaginary parts of the analytic functions are harmonic functions with only two variables. Therefore, this paper proposes the Generalized Cauchy-Riemann equations with n variables by the Jacobian determinant. The Generalized Cauchy-Riemann equations with two variables are extended to n variables as well as the harmonic function. This kind of function has the superiority of conformal orthogonality in three dimensional geometric space.

Key words: Jacobian determinant, generalized Cauchy-Riemann equations, n harmonic function, 3-dimension conformal orthogonality