Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry   of Domains
  This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types.   Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebras 
Vladimir V. Kisil and Debapriya Biswas