Introduction:
Bour's minimal surface is the associated family of Bour's
minimal curve. Note that the Gaussian curvature is invariant under any
rotation about the z axis, even though the surface itself does
not have this property.
Definition:
Note: The exponents on r are (1 + a) and
a.
Properties:
Tangent Planes:
At u = u_{0}, v = v_{0},
the tangent plane to the surface is parameterized by:
[click for formula]

Infinitesimal Area:
The infinitesimal area of a patch on the surface is given by

Gaussian Curvature:


Gaussian curvature of the surface.

Surface colored by Gaussian curvature.


Mean Curvature:


Mean curvature of the surface.

Surface colored by Mean curvature.


