A surface whose curvature lines form an isothermal net. For example, quadrics, surfaces of rotation, surfaces of constant mean curvature, and, in particular, minimal surfaces are isothermal surfaces (cf. Quadric; Rotation surface; Minimal surface). An invariant criterion for a surface to be isothermal is that the Chebyshev vector of the net of curvature lines is gradient. For each isothermal surface one defines another isothermal surface which is, up to a homothety, in conformal Peterson correspondence with it. Inversion of space preserves the class of isothermal surfaces.
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Isothermal surface. I.Kh. Sabitov (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Isothermal_surface&oldid=17906