## Fermions on curved spaces, symmetries, and quantum anomalies

Investigating the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The gravitational and axial anomalies are studied for generalized Euclidean Taub-Newman-Unti-Tamburino (Taub-NUT) metrics, which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. The generalized Taub-NUT metrics exhibit in general gravitational anomalies. Using the Atiyah-Patodi-Singer index theorem for manifolds with boundaries, it is shown that these metrics make no contribution to the axial anomaly.