2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65902In this paper we study Clifford and harmonic analysis on some conformal flat spin manifolds. In particular we treat manifolds that can be parametrized by $U / Γ$ where $U$ is a simply connected subdomain of either $S^{n}$ or $R^{n}$ and $Γ$ is a Kleinian group acting discontinuously on $U$. Examples of such manifolds treated here include for example $RP^{n}$ and $S^{1}\times S^{n-1}$. Special kinds of Clifford-analytic automorphic forms associated to the different choices of $Γ$ are used to construct Cauchy kernels, Cauchy Integral formulas, Green's kernels and formulas together with Hardy spaces, Plemelj projection operators and Szegö kernels for $L^{p}$ spaces of hypersurfaces lying in these manifolds.Analysis of PDEsDifferential Geometry30 G 35, 53 C 27, 42 B 35text