We prove a vanishing theorem for certain isotypical components of the kernel of the S1-equivariant Dirac operator with coefficients in an admissible Clifford module. The method is based on changing the metric by a conformal (generally unbounded) factor and studying the effect of this change on the Dirac operator and its kernel. In the cases relevant to S1-actions we find that the kernel of the new operator is naturally isomorphic to the kernel of the original operator.
All Science Journal Classification (ASJC) codes
- Political Science and International Relations
- Geometry and Topology