## Special Relativity in Complex Space-Time. Part 5. Sketch of the Mathematical Structure of Complex Space-Time

**Authors:** Jozef Radomanski

The article compiles the existing information on complex space-time, from which a sketch of its mathematical structure can be outlined. We divided space-time into geometric and physical layers. The elements of the geometric layer are any four-vectors because, although it is an orthogonal space, it does not have a metrics. The physical layer is created by objects having energy, whose state coordinates are proper or singular paravectors, therefore it is posible to define a metrics for these objects. However, this metrics has no classic properties and it is not a pseudometric of the Minkowski space-time either, so we called it para-metrics. In the physical complex space-time the triangle inequality and the Cauchy inequality have been proved but, however, they have the opposite directions as their equivalents known from Euclidean geometry. At the end, we give a few tips on how to simplify the idea of a complex space-time.

**Comments:** 15 Pages.

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### Submission history

[v1] 2019-02-05 14:47:45

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