Pseudo-Riemannian G₂₍₂₎-manifolds with dimension at most 21

2015/10/22 by Raúl Quiroga-Barranco, Quiroga-Barranco, R.
Mathematics · #20G41 #53C24 #53C50 #57S20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1510.06782

openalex publication_date 2015/10/22 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

Let G₂₍₂₎ be the non-compact connected simple Lie group of type G₂ over ℝ, and let M be a connected analytic complete pseudo-Riemannian manifold that admits an isometric G₂₍₂₎-action with a dense orbit. For the case dim(M) ≤ 21, we provide a full description of the manifold M, its geometry and its G₂₍₂₎-action. The latter are always given in terms of a Lie group geometry related to G₂₍₂₎, and in one case M is essentially the quotient of \widetildeS0₀(3,4) by a lattice.

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