𝐺₂ and the rolling ball

DOI10.1090/S0002-9947-2014-05977-1zbMath1354.20031arXiv1205.2447OpenAlexW2132032311WikidataQ56212892 ScholiaQ56212892MaRDI QIDQ3190799

John Huerta, John C. Baez

Publication date: 19 September 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.2447

zbMATH Keywords

buildingsrolling ballsplit octonions(2, 3, 5) distributionssplit \(\mathrm{G}_{2}\)

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Groups with a (BN)-pair; buildings (20E42) Incidence structures embeddable into projective geometries (51A45) Composition algebras (17A75) Exceptional groups (20G41)

Related Items (17)

Geometrical applications of split octonions ⋮ A Monge normal form for the rolling distribution ⋮ Homogeneous real \((2,3,5)\) distributions with isotropy ⋮ Universal equations for maximal isotropic Grassmannians ⋮ Versal normal form for nonsemisimple singularities ⋮ New relations between G2 geometries in dimensions 5 and 7 ⋮ Cyclic Higgs bundles and minimal surfaces in pseudo-hyperbolic spaces ⋮ Local equivalence of some maximally symmetric rolling distributions and \(SU(2)\) Pfaffian systems ⋮ Dancing polygons, rolling balls, and the Cartan-Engel distribution ⋮ Timelike duality, \(M'\)-theory and an exotic form of the Englert solution ⋮ The algebra of slice functions ⋮ A class of continuous non-associative algebras arising from algebraic groups including ⋮ Flat $\mathfrak{so}(\,p,q)$ -connections for manifolds of non-Euclidean signature ⋮ The contact mappings of a flat \((2,3,5)\)-distribution ⋮ Duality on geodesics of Cartan distributions and sub-Riemannian pseudo-product structures ⋮ Cartan meets Chaplygin ⋮ DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES

Cites Work

• Homogeneous vector bundles
• Buildings and shadows
• Buildings of spherical type and finite BN-pairs
• Rigidity of integral curves of rank 2 distributions
• \(G_2\) and the rolling distribution
• Rolling balls and octonions
• On variational approach to differential invariants of rank two distributions
• Buildings
• The octonions
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