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

Radu Pantilie

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

Differential Geometry 2022-11-02 v7

Authors: Radu Pantilie

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.

Keywords

g-manifolds killing vector fields orbit spaces g2-manifolds spin(7) harmonic morphisms einstein manifolds

Cite

@article{arxiv.2105.07177,
  title  = {On $G_2$-manifolds and geometry in dimensions $6$ and $8$},
  author = {Radu Pantilie},
  journal= {arXiv preprint arXiv:2105.07177},
  year   = {2022}
}

Comments

12 pages, Preprint IMAR, Bucharest, 2021

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