Cauchy Kernels for some Conformally Flat Manifolds

  • John Ryan
Part of the Trends in Mathematics book series (TM)


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.


Conformally flat manifolds surgery Cauchy kernels Dirac operator 

Mathematics Subject Classification (2000)

30G35, 42B30, 53C27, 58J32 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • John Ryan
    • 1
  1. 1.Department of MathematicsUniversity of ArkansasFayettevilleUSA

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