Parallel tractor extension and ambient metrics of holonomy split g_2

C. Robin Graham University of Washington Travis Willse Australian National University

Differential Geometry mathscidoc:1609.10290

Journal of Differential Geometry, 92, (3), 463-505, 2012
The holonomy of the ambient metrics of Nurowski’s conformal structures associated to generic real-analytic 2-plane fields on oriented 5-manifolds is investigated. It is shown that the holonomy is always contained in the split real form G2 of the exceptional Lie group, and is equal to G2 for an open dense set of 2-plane fields given by explicit conditions. In particular, this gives an infinitedimensional family of metrics of holonomy equal to split G2. These results generalize work of Leistner-Nurowski. The inclusion of the holonomy in G2 is established by proving an ambient extension theorem for parallel tractors in the context of conformal geometry in general signature and dimension, which is expected to be of independent interest.
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@inproceedings{c.2012parallel,
  title={PARALLEL TRACTOR EXTENSION AND AMBIENT METRICS OF HOLONOMY SPLIT G_2},
  author={C. Robin Graham, and Travis Willse},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914072625246779952},
  booktitle={Journal of Differential Geometry},
  volume={92},
  number={3},
  pages={463-505},
  year={2012},
}
C. Robin Graham, and Travis Willse. PARALLEL TRACTOR EXTENSION AND AMBIENT METRICS OF HOLONOMY SPLIT G_2. 2012. Vol. 92. In Journal of Differential Geometry. pp.463-505. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914072625246779952.
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