The eta invariant on circle bundles over even-dimensional Fano manifolds equals Zhang's adiabatic limit value for any adiabatic parameter.
Hitchin , Harmonic spinors , Advances in Math., 14 (1974), pp
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The eta invariant of a circle bundle on a Fano manifold
The eta invariant on circle bundles over even-dimensional Fano manifolds equals Zhang's adiabatic limit value for any adiabatic parameter.