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Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry

Biswas D.

Journal of Applied Analysis

2012

Vol. 18, nr 1

145-158

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.