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Complex Hyperbolic 09

ComplexHyperbolic09

Work on illustrations for John Parker's upcoming book "Complex Hyperbolic Kleinian Groups".

ComplexHyperbolic0.5.nb

Math - ComplexHyperbolic09

New in this edition: C-spheres

In general, a C-sphere is a surface in the boundary of hyperbolic space that is topologically a sphere and is foliated by chains (C-circles). One way to specify a C-circle is to give a path in homogeneous coordinates that provides vectors that are normal to the chains. The left picture is given by the path

$\gamma(t) = ( -t^3, \sqrt{2}, t)$

The points corresponding to $t=\pm1$ are $(\pm 1, 0, 0)$ . Taking them to $(0,0,\pm 1)$ produces the picture on the right.

Note: the notebook ComplexHyperbolic0.5 did not draw correct C-spheres, so it's no longer available. The code for the images above will be in CH0.6.

Last Updated on Monday, 20 July 2009 09:17

complexhyperbolic0.4.nb

Math - ComplexHyperbolic09

New in ComplexHyperbolic0.4nb:

The animation of extors changing type (shown in CH0.3.nb post)
A GenerateGroup command for iterating matrix group generators
An example of using R-Balls to build fundamental domains.

The new notebook: ComplexHyperbolic0.4.nb.

Read more... [complexhyperbolic0.4.nb]

ComplexHyperbolic0.3.nb

Math - ComplexHyperbolic09
The notebook has been updated with a proper routine for the Clifford Torus animation (see CH0.2.nb), a quick description of extors, and an animation showing a spinal sphere turning into a fan and then into a Clifford torus. ComplexHyperbolic0.3.nb (right click to play)
Last Updated on Wednesday, 24 June 2009 13:32
Read more... [ComplexHyperbolic0.3.nb]

ComplexHyperbolic0.2.nb

Math - ComplexHyperbolic09
The notebook now has the routines for drawing fans and Clifford tori, objects defined similarly to the spinal spheres:
Last Updated on Friday, 19 June 2009 11:47
Read more... [ComplexHyperbolic0.2.nb]

Some Pictures

Math - ComplexHyperbolic09
Here are some sample pictures ComplexHyperbolic0.1.nb can produce. I'll post better ones later write about the various objects. Cygan Spheres (unit sphere translated, various spheres, various spheres not around 0)
Last Updated on Monday, 01 June 2009 23:32
Read more... [Some Pictures]

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