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arXiv · 2601.06756

New Calabi-Yau Metrics of Taub-NUT Type on C^{N+1}

Tengfei Ma
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Abstract

We construct a class of complete non-flat Calabi-Yau metrics on C^{N+1} for every N >= 3, which generalize the Taub-NUT metrics from C^2 and C^3 and whose tangent cone at infinity is R^N. 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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Tengfei Ma. 2026-01-11. New Calabi-Yau Metrics of Taub-NUT Type on C^{N+1}. https://arxiv.org/abs/2601.06756

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