The Dirac operator on generalized Taub-NUT spaces

Details The Dirac operator on generalized Taub-NUT spaces The Dirac operator on generalized Taub-NUT spaces

2010-03-28

arxiv.org/abs/1003.5364v2

Commun. Math. Phys. 305, 641-656 (2011)

Mathematics

Differential Geometry

Final version, 16 pages

Scientific paper

10.1007/s00220-011-1263-4

We find sufficient conditions for the absence of harmonic $L^2$ spinors on
spin manifolds constructed as cone bundles over a compact K\"ahler 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.

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