HYPERBOLIC DIRAC AND LAPLACE OPERATORS ON EXAMPLES OF HYPERBOLIC SPIN MANIFOLDS

Fundamental solutions of hyperbolic Dirac operators and hyperbolic versions of the Laplace operator are introduced for a class of conformally flat manifolds. This class consists of manifolds obtained by factoring out upper half-space of R-n by arithmetic subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented together with associated Eisenstein and Poincare type series. As main goal we develop Cauchy and Green type integral formulas and describe Hardy space decompositions for spinor sections of the associated spinor bundles on these manifolds.