On $G_2$-manifolds and geometry in dimensions $6$ and $8$

Radu Pantilie

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arXiv · 2105.07177

On $G_2$-manifolds and geometry in dimensions $6$ and $8$

Radu Pantilie

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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 $G={\rm Spin}(7)$ 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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BibTeX RIS

Radu Pantilie. 2021-05-15. On $G_2$-manifolds and geometry in dimensions $6$ and $8$. https://arxiv.org/abs/2105.07177

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