Cartan's incomplete classification and an explicit ambient metric of holonomy \(\mathrm G_2^\ast\)

DOI10.1007/s40879-017-0178-9zbMath1403.53045arXiv1411.7172OpenAlexW2963412556WikidataQ59607645 ScholiaQ59607645MaRDI QIDQ723354

Travis Willse

Publication date: 31 July 2018

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7172

zbMATH Keywords

conformal geometrygeneric distributionsexceptional holonomy\((2, 3, 5)\) distributions\(\mathrm G_2\)Fefferman-Graham ambient constructionmetric holonomy

Mathematics Subject Classification ID

Exterior differential systems (Cartan theory) (58A15) Issues of holonomy in differential geometry (53C29) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (5)

A Monge normal form for the rolling distribution ⋮ Homogeneous real \((2,3,5)\) distributions with isotropy ⋮ Local type I metrics with holonomy in \(\mathrm{G}_2^\ast\) ⋮ Local equivalence of some maximally symmetric rolling distributions and \(SU(2)\) Pfaffian systems ⋮ The contact mappings of a flat \((2,3,5)\)-distribution

Cites Work

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• Conformal holonomy equals ambient holonomy
• The geometry of almost Einstein \((2,3,5)\) distributions
• Ambient metrics for \(n\)-dimensional \(pp\)-waves
• Rigidity of integral curves of rank 2 distributions
• Parallel tractor extension and ambient metrics of holonomy split \(G_2\)
• \(G_2\) and the rolling distribution
• Rolling balls and octonions
• Twistor space for rolling bodies
• On variational approach to differential invariants of rank two distributions
• Differential equations and conformal structures
• Highly symmetric 2-plane fields on 5-manifolds and 5-dimensional Heisenberg group holonomy
• Ambient metrics with exceptional holonomy
• The Ambient Metric (AM-178)
• A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS
• Fefferman–Graham ambient metrics of Patterson–Walker metrics
• Nearly Kahler geometry and (2,3,5)-distributions via projective holonomy
• Conformal Structures with Explicit Ambient Metrics and Conformal G 2 Holonomy
• A Theorem on Holonomy

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