Essays about: "Hyperbolic plane"
Showing result 1 - 5 of 6 essays containing the words Hyperbolic plane.
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1. Expanding flows of curves in the hyperbolic plane
University essay from Uppsala universitet/Tillämpad matematik och statistikAbstract : .... READ MORE
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2. Always Look on the Positive-Definite Side of Life
University essay from Göteborgs universitet/Institutionen för matematiska vetenskaperAbstract : This thesis concerns distributions on Rn with the property of being positive-definite relative to a finite subgroup of the orthogonal group O(n). We construct examples of such distributions as the inverse Abel transform of Dirac combs on the geometries of Euclidean space Rn and the real- and complex hyperbolic plane H2, H2 C. READ MORE
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3. The 2+1 Lorentz Group and Its Representations
University essay from Stockholms universitet/FysikumAbstract : The Lorentz group is a symmetry group on Minkowski space, and as such is central to studying the geometry of this and related spaces. The group therefore shows up also from physical considerations, such as trying to formulate quantum physics in anti-de Sitter space. READ MORE
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4. Algorithmic Construction of Fundamental Polygons for Certain Fuchsian Groups
University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakultetenAbstract : The work of mathematical giants, such as Lobachevsky, Gauss, Riemann, Klein and Poincaré, to name a few, lies at the foundation of the study of the highly structured Riemann surfaces, which allow definition of holomorphic maps, corresponding to analytic maps in the theory of complex analysis. A topological result of Poincaré states that every path-connected Riemann surface can be realised by a construction of identifying congruent points in the complex plane, the Riemann sphere or the hyperbolic plane; just three simply connected surfaces that cover the underlying Riemann surface. READ MORE
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5. On Poicarés Uniformization Theorem
University essay from Matematiska institutionenAbstract : A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$. READ MORE
