Some conformally flat spin manifolds, Dirac operators and automorphic forms

摘要

In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/Gamma where U is a subdomain of either S-n or R-n and Gamma is a Kleinan group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S-1 X s(n-1). Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of F are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Pleme1j projection operators for LP spaces of hypersurfaces lying in these manifolds. (c) 2006 Elsevier Inc. All rights reserved.