2009/11/05 by Bogdan G. Dimitrov, Dimitrov, Bogdan G.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0911.1052
18 pages; no figures; submitted to "Journal of Geometry and Physics"
arxiv created 2009/11/05 · openalex publication_date 2009/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The third part of the present paper continues the investigation of the solution of the multivariable cubic algebraic equation for reparametrization invariance of the gravitational Lagrangian. The main result in this paper constitutes the fact that the earlier found parametrization functions of the cubic algebraic equation for reparametrization invariance of the gravitational Lagrangian can be considered also as uniformization functions. These functions are obtained as solutions of first - order nonlinear differential equations, as a result of which they depend only on the complex (uniformization) variable z. Further, it has been demonstrated that this uniformization can be extended to two complex variables, which is particularly important for investigating various physical metrics, for example the ADS metric of constant negative curvature (Lobachevsky spaces).