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Dirac and Laplace operators on some non-orientable conformally flat manifolds

By Rolf Sören Krausshar

Abstract

In this paper we present an explicit construction for the fundamental solution to the Dirac and Laplace operator on some non-orientable conformally flat manifolds. We first treat a class of projective cylinders and tori where we can study monogenic sections with values in different pin bundles. Then we discuss the M\"obius strip, the Klein bottle and higher dimensional generalizations of them. We present integral representation formulas together with some elementary tools of harmonic analysis on these manifolds.Comment: 22 page

Topics: Mathematics - Differential Geometry, Mathematics - Complex Variables, Mathematics - Geometric Topology, 30G35, 53C21, 53C27
Year: 2011
OAI identifier: oai:arXiv.org:1102.4251
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