The Dirac equation on metrics of Eguchi-Hanson type

We investigate parallel spinors on the Eguchi-Hanson metrics and find the space of complex parallel spinors is complex two-dimensional. For the metrics of Eguchi-Hanson type with the zero scalar curvature, we separate variables for the harmonic spinors and obtain the solutions explicitly.

Automated summary

We study parallel spinors on the Eguchi-Hanson metrics and find that the space of complex parallel spinors is complex two-dimensional. For the metrics of Eguchi-Hanson type with zero scalar curvature, we separate variables for the harmonic spinors and obtain explicit solutions.