Aarhus Universitets segl

Construction of higher dimensional ALF Calabi-Yau metrics

Daheng Min (University of Münster)
Tirsdag 19. maj 2026 11:00 – 11:50 Aud. G2 (1532-122)
Workshop

Roughly speaking, an ALF metric of real dimension 2n should be a complete metric such that its asymptotic cone is of dimension 2n-1, the volume growth of this metric is of the order of 2n-1 , and its sectional curvature tends towards 0 near infinity. I will give examples of ALF Calabi–Yau metrics of real dimension greater than 4. Our first example is that the Taub–NUT deformation of a hyperkählerian cone with respect to a locally free circle action is hyperkählerian ALF. The second example is that a special class of complete Calabi–Yau metrics on C^n, constructed by Apostolov and Cifarelli, is ALF. Based on these examples, I will explain how to produce more ALF Calabi–Yau metrics on some resolutions of known examples modeled on them. In particular, there exist ALF Calabi–Yau metrics on the canonical bundles of classical homogeneous Fano contact manifolds.

Organiseret af: CMCG
Kontakt: Cristiano Spotti Revideret: 16.05.2026