2013/01/23 by A. V. Nazarenko, Nazarenko, A. V.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1301.5446
12 pages, 4 figures
arxiv created 2013/01/23 · openalex publication_date 2013/01/23 · arxiv updated 2013/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is explored a model of compact Riemann surfaces in genus two, represented geometrically by two-parametric hyperbolic octagons with an order four automorphism. We compute the generators of associated isometry group and give a real-analytic description of corresponding Teichmüller space, parametrized by the Fenchel-Nielsen variables, in terms of geometric data. We state the structure of parameter space by computing the Weil-Petersson symplectic two-form and analyzing the isoperimetric orbits. The results of the paper may be interesting due to their applications to the quantum geometry, chaotic systems and low-dimensional gravity.