Abstract
We analyse the behaviour of the Euclidean Dirac operator under a special transformation preserving monogenicity. The framework of Vahlen matrices (seeAhlfors, Maks) provides the tools for such a treatment. We show that the conjugate of the Dirac operator with respect to such a transformation leads to a first order operator on a Riemannian manifold with a weighed metric and present some properties of such an operator. An explicit construction is done, using the Cayley transformation.
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