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Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry
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Debapriya Biswas
Published/Copyright:
June 5, 2012
Abstract.
The result that the upper half plane is not preserved in the hyperbolic case has implications in physics, geometry and analysis. We discuss in details the introduction of projective coordinates for the EPH cases. We also introduce an appropriate compactification for all the three EPH cases, which results in a sphere in the elliptic case, a cylinder in the parabolic case and a crosscap in the hyperbolic case.
Keywords: EPH cases; projective coordinates; compactification; Möbius transformation; Clifford algebra; Lie group
Received: 2010-11-03
Revised: 2011-05-26
Accepted: 2011-06-16
Published Online: 2012-06-05
Published in Print: 2012-06-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
EPH cases;
projective coordinates;
compactification;
Möbius transformation;
Clifford algebra;
Lie group
Articles in the same Issue
- Masthead
- Regularity theory for superquadratic energy functionals related to nonlinear Hencky materials in three dimensions
- Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation
- Perturbations of the matrix logarithm
- Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems
- Results of Tadeusz Świa̧tkowski on algebraic sums of sets and their applications in the theory of subadditive functions
- The generalized Stokes theorem for ℝ-linear forms on Lie algebroids
- Certain classes of multivalent functions with negative coefficients involving the Hadamard product
- Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry
- Location of zeros of polynomials
