2006/09/05 by G. I. Garas'ko, Garas'ko, G. I., D. G. Pavlov +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0609009
10 pages
arxiv created 2006/09/05 · openalex publication_date 2006/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The space of the associative commutative hyper complex numbers, H4, is a 4-dimensional metric Finsler space with the Berwald-Moor metric. It provides the possibility to construct the tensor fields on the base of the analytical functions of the H4 variable and also in case when this analyticity is broken. Here we suggest a way to construct the metric tensor of a 4-dimensional pseudo Riemannian space (space-time) using as a base the 4-contravariant tensor of the tangent indicatrix equation of the Berwald-Moor space and the World function. The Berwald-Moor space appears to be closely related to the Minkowski space. The break of the analyticity of the World function leads to the non-trivial curving of the 4-dimensional space-time and, particularly, to the Newtonian potential in the non-relativistic limit.