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Clifford analysis on spheres and hyperbolae. (English) Zbl 0909.30007

The consideration of Dirac operators over general manifolds is of great importance in different fields of applications, especially in geometry. Using Vahlen matrices the author succeeds to carry over a lot of results developed in in real Clifford analysis in \(\mathbb R^n\) to the sphere and the hyperbola. It seems to be one of the first papers which use Clifford analysis in the Minkowski space. I believe that it is a decisive step towards a general Clifford analysis in Krein spaces. Among other results the author proves the conformal covariance of the Dirac operator using the spin group associated to \(\mathbb R^{n,1}\).

MSC:

30C35 General theory of conformal mappings
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
53C27 Spin and Spin\({}^c\) geometry
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