Work

Nearly Parallel $\mathrm{G}_{2}$-Structures with Torus Symmetry

Year: 2025

Type: preprint

Abstract: We study nearly parallel $\mathrm{G}_{2}$-structures with a three-torus symmetry via multi-moment map techniques. An effective three-torus action on a nearly parallel $\mathrm{G}_{2}$-manifold yields a multi-moment map. The torus acts freely on its regular level sets, so they are torus bundles over smooth three-dimensional manifolds. We show that the geometry of the base spaces is specified by two triples of closed two-forms related by a Riemannian metric. We then describe an inverse construction producing invariant nearly parallel $\mathrm{G}_{2}$-structures from three-dimensional data. We observe that locally this may produce examples with four-torus symmetry.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2508.21703

Authors: Russo, Giovanni, Swann, Andrew

Institutions: Scuola Internazionale Superiore di Studi Avanzati, Aarhus University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Award: G5245466801

OpenAlex ID: W4415993198

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