Complete non-compact $\operatorname{Spin}(7)$-manifolds from $T^2$-bundles over AC Calabi Yau manifolds

Autor:	Cavalleri, Nicolò
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry 53C10 53C25 53C29 53C80
Druh dokumentu:	Working Paper
Popis:	We develop a new construction of complete non-compact 8-manifolds with Riemannian holonomy equal to $\operatorname{Spin}(7)$. As a consequence of the holonomy reduction, these manifolds are Ricci-flat. These metrics are built on the total spaces of principal $T^2$-bundles over asymptotically conical Calabi Yau manifolds. The resulting metrics have a new geometry at infinity that we call asymptotically $T^2$-fibred conical ($AT^2C$) and which generalizes to higher dimensions the ALG metrics of 4-dimensional hyperk\"ahler geometry, analogously to how ALC metrics generalize ALF metrics. As an application of this construction, we produce infinitely many diffeomorphism types of $AT^2C$ $\operatorname{Spin}(7)$-manifolds and the first known example of complete toric $\operatorname{Spin}(7)$-manifold. Comment: 49 pages, no figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.19486 Zobrazit plný text záznamu View this record from Arxiv