New Calabi-Yau Metrics of Taub-NUT Type on CN+1
Abstract
We construct a class of complete non-flat Calabi-Yau metrics on CN+1 for every N >= 3, which generalize the Taub-NUT metrics from C2 and C3 and whose tangent cone at infinity is RN. The construction relies on the generalized Gibbons-Hawking ansatz. A key obstacle is that the volume-form defect of the ansatz fails to decay near certain components of the discriminant locus, producing singularities more severe than those encountered in dimension three, we resolve this by a gluing procedure.
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