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Hyperbolic Geometry
Clarence Kineider (Max Planck Society, Max Planck Institute for Mathematics in the Sciences), Georgios Kydonakis (University of Patras), Eugen Rogozinnikov (Korea Institute for Advanced Study), Valdo Tatitscheff (Technical University of Munich), Alexander Thomas (Lyon 1 Université)
Abstract: Abstract Every compact surface admits a constant curvature metric, endowing it with a geometry. For surfaces of genus at least 2, this leads to hyperbolic geometry. The model space is the hyperbolic plane. We give a brief introduction to the beautiful world of hyperbolic geometry in dimension 2 starting from the hyperbolic plane and its isometries and then discussing hyperbolic surfaces. References for an extended treatment include, for example, Thurston (Collected works of William P. Thurston with commentary: IV. The geometry and topology of three-manifolds: with a preface by Steven P. Kerckhoff, 2022 ) or Benedetti and Petronio (Lectures on hyperbolic geometry, 1992); Marden (Hyperbolic manifolds. An introduction in 2 and 3 dimensions, 2016); Ramsay and Richtmyer (Introduction to hyperbolic geometry, 1995).