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The Helicoid with Handle(s) |
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Hoffman, Karcher and Wei added handles to the helicoid. All the pictures on this page are made using
VRML models of the surfaces by J. Hoffman. |
| The most simple of these surfaces is the singly periodic helicoid which is invariant under a translation
so that the quotient surface has genus one (compare this to Riemann's minimal surface). It contains several straight lines: There is a horizontal line which is invariant under the translation and there are also two further lines within a fundamental piece hich are orthogonal to the horizontal line. |
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| This surface admits a twist deformation.
The twist angle is the angle by which the surface normal turns around when moving along the horizontal straight
line in a fundamental piece. The twist angle can be less then 2 pi, squeezing the surface.More importantly,
it can be arbitrarily large. |
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| For infinite twist angle, these surfaces converge to the genus one helicoid.
This is the first example of an infinite total curvature but finite topology embedded minimal surface. |
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