On the incompleteness of $G_2$-moduli spaces along degenerating families of $G_2$-manifolds

Autor:	Langlais, Thibault
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry 53C26 (Primary) 53C29 53A15 58D27 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We derive a formula for the energy of a path in the moduli space of a compact $G_2$-manifold with vanishing first Betti number for the volume-normalised $L^2$-metric. This allows us to give simple sufficient conditions for a path of torsion-free $G_2$-structures to have finite energy and length. We deduce that the compact $G_2$-manifolds produced by the generalised Kummer construction have incomplete moduli spaces. Under some assumptions, we also state a necessary condition for the limit of a path of torsion-free $G_2$-structures to be at infinite distance in the moduli space. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.02943 Zobrazit plný text záznamu View this record from Arxiv