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By Redei L.
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10] D. G. Pavlov, Nonlinear relativistic invariance for quadrahyperbolic numbers, arXiv: gr-qc/0212090.  D. G. Pavlov, Four-dimensional time as alternative to Minkowski space-time, Proceedings of International Conference ”GEON-2003”, Kazan, 2003.  D. G. Pavlov, Chronometry of the three-dimensional time, Hypercomplex Numbers in Geometry and Physics, 1, Vol 1, 2004.  G. Yu. Bogoslovskiy, Status and Perspectives of Theory of Local Anisotropic SpaceTime, Physics of Nuclei and Particles.
The circumference that belongs to two light cones, that is corresponds to the interception of the pseudo-Euclidean sphere with R = 0 which in the Special Theory of Relativity is interpreted as a momentary position of the light front, that can be registered by the observer that is at the top of one of the cones, supposing that there is a flash at the top of the other. In general we should apply an analogous interpretation to the three-dimensional time case. So, the broken hexagon depicted on Fig.
An 47 (2) where ni=1 ai = 1. The corresponding reflections can be classified as Hyperbolic turn (that in a way are analogous to the busts of the pseudo-Euclidean spaces) because such transformations leave on the place a point of convergence of the tops of all the pyramids and isotropic edges of the last at the same time turn into themselves. Among continuous movements of the multy-dimensional time along with hyperboloic turns there is also a n-parametrical subgroup of parallel transfers. The examined variety doesn’t include any other continuous congruent transformations and that is why has less freedom than the spaces with quadratic types of metrics.
Algebra, Vol.1 by Redei L.