Aspects of Dirac Operators in Analysis

摘要

We give a review of the analysis behind several examples of Dirac-type operators over manifolds arising in Clifford analysis. These include the Atiyah-Singer-Dirac operator acting on sections of a spin bundle over a spin manifold. It also includes several Dirac operators arising over conformally flat spin manifolds including hyperbolic space. Links to classical harmonic analysis are pointed out.