Construction of higher-dimensional ALF Calabi-Yau metrics

2023/06/02 by Min, Daheng · 1 citation
#53C25 (Primary) 53C55 #53C26 #53C30 #53D20 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.01866

Abstract

Roughly speaking, an ALF metric of real dimension 4n should be a metric such that it has a (4n-1)-dimensional asymptotic cone, the volume growth of this metric is of order 4n-1 and its sectional curvature tends to 0 at infinity. In this paper, we first show that the Taub-NUT deformation of a hyperkähler cone with respect to a locally free S1-symmetry is ALF hyperkähler. Using this metric at infinity, we establish the existence of ALF Calabi-Yau metric on certain crepant resolutions. In particular, we prove that there exist ALF Calabi-Yau metrics on canonical bundles of classical homogeneous Fano contact manifolds.

Cited by

• Géométrie à l'infini des variétés hyperkählériennes toriques

Related

• Warped quasi-asymptotically conical Calabi-Yau metrics
• Asymptotically conical Calabi-Yau metrics on quasi-projective varieties
• Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity
• Classification of asymptotically conical Calabi-Yau manifolds
• Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones