Cauchy Kernels for some Conformally Flat Manifolds
Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the sphere S n . For such manifolds we shall introduce a Cauchy kernel, Cauchy integral formula for sections taking values in a spinor bundle and annihilated by a Dirac operator, or generalized Cauchy-Riemann operator. Basic properties of this kernel are examined. We also introduce a Green’s kernel and a Green’s formula for harmonic sections in this context.
KeywordsConformally flat manifolds surgery Cauchy kernels Dirac operator
Mathematics Subject Classification (2000)30G35, 42B30, 53C27, 58J32
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