2013/09/20 by D. M. Volokitin, Volokitin, D. M.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #advanced mathematical theories #math.GM
paper · pdf · doi:10.48550/arxiv.1501.04069
arxiv created 2013/09/20 · openalex publication_date 2013/09/20 · arxiv updated 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper the certain 4-dimensional algebra in 4-dimensional pseudo-Riemannian space with signature (1, -1, -1, -1) is constructed. On the basis of this algebra the elements of the analysis, i.e. the theory of 4-dimensional functions of the 4-dimensional variable are built up. In the process of designing the analysistwo additional assumptions aboutthe properties of functions are made. Obtained under different assumptionsabout the properties of functions, the Cauchy-Riemann equations are solved in flat, spherically and cylindrically symmetric cases. In the cylindrically symmetric case the wave solutions were obtained both for the metric tensor and for the 4-dimensional function. Both waves spreadwith the speed equal to unity along null geodesics. The properties of the metric tensor as physically real object are postulated, but the idea what the 4-dimensional function (vector field) is remains unclear.