Dirac operators on spheres and hyperbolae. (English) Zbl 0894.30031

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 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 Krein spaces. 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 \(\mathbb{R}^{n,1}\).


30G35 Functions of hypercomplex variables and generalized variables
53C27 Spin and Spin\({}^c\) geometry