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Cauchy kernels for some conformally flat manifolds

John Ryan
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Abstract

Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the n-dimensional sphere. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections tasking values in a spinor bundle and annihilated by a Dirac operator, or generalized Cauchy-Riemann operator. Basic properties of this kernel are examined, in particular we examine links to Hardy spaces.

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John Ryan. 2003-03-26. Cauchy kernels for some conformally flat manifolds. https://arxiv.org/abs/math/0303341

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