PDF Articles for Cartan's Corner 
Links to Maple programs

Lorentz MapsClick 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 TransformationsClick 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 2forms.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 2forms and Cartan Curvature 2forms are globally zero. The topological feartures of the 3D spatial subspace are examined.Parametric SurfacesClick on parametric.zip which is a zipped Maple V program to evaluate numerous versions of parametric N1 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 2surface in 4D.
Implicit SurfacesClick 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. 