Isothermal net
From Encyclopedia of Mathematics
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An orthogonal net on a surface $V^2$ in Euclidean $3$-space in which the small quadrangles formed by two pairs of lines from distinct families are, up to infinitesimal quantities of the first order, squares. The lines of an isothermal net are level curves of two conjugate harmonic functions. In the parameters of an isothermal net the line element has the form:
$$ds^2=\lambda^2(du^2+dv^2),$$
where $\lambda=\lambda(u,v)$. An isothermal net is a particular case of a rhombic net. On a surface of rotation the meridians and parallels form an isothermal net; an asymptotic net on a minimal surface is isothermal.
Comments
See also Isothermal coordinates and the references given there.
How to Cite This Entry:
Isothermal net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Isothermal_net&oldid=32394
Isothermal net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Isothermal_net&oldid=32394
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article