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There exist exactly four homomorphisms from the pseudo-orthogonal group of index one into the group of real numbers Thus we have four -spaces of -scalars in the geometry of the group The group operates also on the sphere forming a -space of isotropic directions In this note, we have solved the functional equation for given independent points with and an arbitrary matrix considering each of all four homomorphisms. Thereby we have determined all equivariant mappings
We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups and , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective...
The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
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