Lorentz Maps
Click on Lorentz.zip which is a zipped
Maple program to evaluate numerous versions of Lorentz maps. The Lorentz map is
defined as the transformation that preserves the quadratic form with Minkowski
signature. (The Eikonal -- whose zero set defines the domain of discontinuous
solutions to Maxwell's equations.) The parameters are not presumed to be global
constants hence the method can be applied to accelerating frames of reference.
Affine Transformations
Click on affine.zip which is a zipped Maple
V program to evaluate numerous versions of affine transformations on a 4 D
variety. There are two species of affine maps: the PA Particle Affine map and
the WA Wave affine map. The PA map in 4D has three zeros on the bottom row,
where the WA mnap has three zeros on the RH column.
A4 Spaces of Zero Cartan Torsion and Curvature 2-forms.
Click on a4space.zip which is a zipped
Maple V program to evaluate numerous versions of A4 spaces, which are 4D space
for which the Cartan torsion 2-forms and Cartan Curvature 2-forms are globally
zero. The topological feartures of the 3D spatial subspace are examined.
Parametric Surfaces
Click on parametric.zip which is a
zipped Maple V program to evaluate numerous versions of parametric N-1 surfaces
in N space. The Cartan Torsion and Curvature 2- forms are evaluated, along
with the mean curvature and the classic Gauss curvature. Numerous examples are
computed for 2 parametr surfaces in R3. Also the Klein Bottle is demonstrated
as a 2-surface in 4D.
Implicit Surfaces
Click on implinor.zip which is a zipped
Maple V program to evaluate numerous versions of implicit surfaces. The Cartan
Torsion and Curvature 2- forms are evaluated, along with the mean curvature and
the classic Gauss curvature. The relationship between the shape matrix and the
Jacobian of the normalized gradient to the implicit surface is utilized to
compare the the properties of different surfaces. These results are to be
compared to the parametric methods.
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