Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds

Ilka Agricola; Simon G. Chiossi; Thomas Friedrich; Jos Höll

doi:10.1016/j.geomphys.2015.08.023

Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds

Differential Geometry 2015-12-09 v2 Mathematical Physics math.MP

Authors: Ilka Agricola , Simon G. Chiossi , Thomas Friedrich , Jos Höll

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We present a uniform description of $\mathrm{SU}(3)$ -structures in dimension $6$ as well as $G_2$ -structures in dimension $7$ in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to hypersurface theory to obtain new embedding theorems, and give a general recipe for building conical manifolds. The approach also enables one to subsume all variations of the notion of a Killing spinor.

Keywords

SU(3)-structures G_2-structures characterising spinor spinorial field equations hypersurface theory embedding theorems conical manifolds Killing spinor

Cite

@article{arxiv.1411.5663,
  title  = {Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds},
  author = {Ilka Agricola and Simon G. Chiossi and Thomas Friedrich and Jos Höll},
  journal= {arXiv preprint arXiv:1411.5663},
  year   = {2015}
}

Comments

25 pages; typos and misprints corrected; to appear in Journal of Geometry and Physics

Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds

Abstract

Keywords

Cite

Comments

Related papers