  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.
