2024/07/28 by Nicolò Cavalleri, Cavalleri, Nicolò
Mathematics · #53C10 #53C25 #53C29 #53C80 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2407.19486
openalex publication_date 2024/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new construction of complete non-compact 8-manifolds with Riemannian holonomy equal to Spin(7). As a consequence of the holonomy reduction, these manifolds are Ricci-flat. These metrics are built on the total spaces of principal T2-bundles over asymptotically conical Calabi Yau manifolds, and the result is generalized to orbifolds. The resulting metrics have a new geometry at infinity that we call asymptotically T2-fibred conical (AT2C) and which generalizes to higher dimensions the ALG metrics of 4-dimensional hyperkähler geometry, analogously to how ALC metrics generalize ALF metrics. As an application of this construction, we produce infinitely many diffeomorphism types of AT2C Spin(7)-manifolds and the first known examples of complete toric Spin(7)-manifold.