Junior Seminar: Hyperbolic Geometry Lecture Notes
نویسنده
چکیده
Our first construction is very similar in spirit to an analogous one in Euclidean space. The group of isometries of Euclidean R is given by O(n) ⊕ R or SO(n) ⊕ R if we want to preserve orientation; the first factor is made up of rotations and reflections (in the non-orientation-preserving case) about the origin, while the second factor gives translations. Now, it turns out that O(n) is generated by reflections. What is a reflection?
منابع مشابه
Degenerations of Hyperbolic Structures on Surfaces
These are lecture notes from the summer school on Geometry, Topology and Dynamics of Character Varieties at the Institute for Mathematical Sciences, National University of Singapore in July of 2010. The objective is to give an introduction to some of the tools used in studying the degeneration of hyperbolic structures on surfaces as developed by Thurston, and in particular to describe his const...
متن کاملHyperbolic structures on surfaces and geodesic currents
These are lecture notes for a course given by the authors during the program Automorphisms of Free Groups: Geometry, Topology, and Dynamics, held at the CRM (Barcelona) in 2012. The main objective of the notes is to describe Bonahon’s construction of Thurston’s compactification of Teichmüller space, in terms of geodesic currents on surfaces. In the final section, we present several extensions o...
متن کاملLecture Notes. Waves in Random Media
Contents 1 Wave equations and First-order hyperbolic systems 4 1.
متن کاملRealizability as the Connection between Computable and Constructive Mathematics
These are lecture notes for a tutorial seminar which I gave at a satellite seminar of “Computability and Complexity in Analysis 2004” in Kyoto. The main message of the notes is that computable mathematics is the realizability interpretation of constructive mathematics. The presentation is targeted at an audience which is familiar with computable mathematics but less so with constructive mathema...
متن کاملInfimum of the spectrum of Laplace-Beltrami operator on a bounded pseudoconvex domain with a Kähler metric of Bergman type
where dVg is the volume measure on M with respect to the Kähler metric g. When M is compact and ∆g is uniformly elliptic, λ1(∆g) is the first positive eigenvalue of ∆g with Dirichlet boundary condition. A lot of research has been done on its upper and lower bound estimates and its impact on geometry and physics (see for examples, the lecture notes of P. Li [8] and the paper of S. Udagawa [16] a...
متن کامل