Article Dans Une Revue Journal of Geometry and Physics Année : 2026

A local generalisation of frame bundles

Jérémie Pierard de Maujouy

Résumé

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame bundles as a smooth manifold equipped with a coframe with value in a suitable Lie algebra and which furthermore satisfies a weakened version of the Maurer-Cartan equation. From this structure it is possible to construct a Lie algebra action on the manifold. We study the question of whether it is possible to construct a Lie group action and build a base manifold over which the initial manifold is a frame bundle. We find that generalised frame bundles can have singular underlying manifolds.

Dates et versions

hal-05396913 , version 1 (03-12-2025)

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Citer

Jérémie Pierard de Maujouy. A local generalisation of frame bundles. Journal of Geometry and Physics, 2026, 223, pp.105782. ⟨10.1016/j.geomphys.2026.105782⟩. ⟨hal-05396913⟩
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