On <i>G</i><sub>2</sub>-manifolds and geometry in dimensions 6 and 8

Abstract We study the geometry induced on the local orbit spaces of Killing vector fields on (Riemannian) $G$ -manifolds, with an emphasis on the cases $G=\textrm {Spin}(7)$ and $G=G_2$ . Along the way, we classify the harmonic morphisms with one-dimensional fibres from $G_2$ -manifolds to Einstein manifolds.

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Publication Details

Journal
Glasgow Mathematical Journal
Published
2025-08-12
DOI
https://doi.org/10.1017/s0017089525100670
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
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article

On G2-manifolds and geometry in dimensions 6 and 8

Radu Pantilie
Glasgow Mathematical Journal
Geometric Analysis and Curvature Flows
article

On G2-manifolds and geometry in dimensions 6 and 8

Radu Pantilie
article en

Abstract

Abstract We study the geometry induced on the local orbit spaces of Killing vector fields on (Riemannian) $G$ -manifolds, with an emphasis on the cases $G=\textrm {Spin}(7)$ and $G=G_2$ . Along the way, we classify the harmonic morphisms with one-dimensional fibres from $G_2$ -manifolds to Einstein manifolds.

Glasgow Mathematical Journal
Openalex Percentile: Top 70%
Geometric Analysis and Curvature Flows
DOISourceOpenAlex
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