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Isothermal Parameterization

A parameterization is isothermal if, for $\zeta\equiv u+iv$ and

\begin{displaymath}
\phi_k(\zeta)={\partial x_k\over\partial u}-i{\partial x_k\over\partial v},
\end{displaymath}

the identity

\begin{displaymath}
{\phi_1}^2(\zeta)+{\phi_2}^2(\zeta)+{\phi_3}^2(\zeta)=0
\end{displaymath}

holds.

See also Minimal Surface, Temperature




© 1996-9 Eric W. Weisstein
1999-05-26