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Some conformally flat spin manifolds, Dirac operators and automorphic forms. (English) Zbl 1107.30037

The authors continue their research on function theory on conformally flat manifolds in higher dimensions [see Rev. Mat. Iberoam. 21, 87–110 (2005; Zbl 1079.30067)]. Here they deal with real projective spaces, with cylinders and tori, and with manifolds of the form \(S^1\times S^{n-1}\). They give the respective Cauchy kernel und Cauchy’s integral formula. The manifolds are defined by \(U/\Gamma\) where \(U\) is a domain \(U\) in \(S^n\) or \(\mathbb{R}^n\) and \(\Gamma\) is a Kleinian group. Some applications are given.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
31C12 Potential theory on Riemannian manifolds and other spaces
30D55 \(H^p\)-classes (MSC2000)

Citations:

Zbl 1079.30067
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References:

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