The Dirac operator on generalized Taub-NUT spaces

Abstract

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.

Final version, 16 pages

References in corpus (3)

• Gravitational and axial anomalies for generalized Euclidean Taub-NUT metrics
• $L^2$-index of the Dirac operator of generalized Euclidean Taub-NUT metrics
• The Dirac spectrum on manifolds with gradient conformal vector fields

Cited by in corpus (2)

• Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
• Transverse Killing and twistor spinors associated to the basic Dirac operators