Some Conformally Flat Spin Manifolds, Dirac Operators and Automorphic Forms

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In 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.

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Analysis of PDEs, Differential Geometry, 30 G 35, 53 C 27, 42 B 35

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http://salesiana.dossiersoluciones.com/handle/123456789/65902

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0212086
 http://arxiv.org/abs/math/0212086

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arXiv