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Type: Journal article
Title: New relations between G₂ geometries in dimensions 5 and 7
Other Titles: New relations between G(2) geometries in dimensions 5 and 7
Author: Leistner, T.
Nurowski, P.
Sagerschnig, K.
Citation: International Journal of Mathematics, 2017; 28(13):1750094-1-1750094-46
Publisher: World Scientific
Issue Date: 2017
ISSN: 0129-167X
Statement of
Thomas Leistner, Paweł Nurowski, Katja Sagerschnig
Abstract: There are two well-known parabolic split G₂ geometries in dimension 5, (2, 3, 5) distributions and G₂ contact structures. Here we link these two geometries with yet another G₂ related contact structure, which lives on a 7-manifold. More precisely, we present a natural geometric construction that associates to a (2, 3, 5) distribution a 7-dimensional bundle endowed with a canonical Lie contact structure. We further study the relation between the canonical normal Cartan connections associated with the two structures and we show that the Cartan holonomy of the induced Lie contact structure reduces to G₂. This motivates the study of the curved orbit decomposition associated with a G₂ reduced Lie contact structure on a 7-manifold. It is shown that, provided an additional curvature condition is satisfied, in a neighborhood of each point in the open curved orbit the structure descends to a (2, 3, 5) distribution on a local leaf space. The closed orbit carries an induced G₂ contact structure.
Keywords: (2, 3, 5) distribution; lie contact structure; parabolic geometry; Cartan connection; G₂
Rights: © World Scientific Publishing Company
DOI: 10.1142/S0129167X1750094X
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Mathematical Sciences publications

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