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Parallel tractor extension and ambient metrics of holonomy split G 2

Graham, C R; Willse, Travis


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...[Show more]

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Journal of Differential Geometry


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