Bour's Minimal Surface

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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 = u0, v = v0, 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.