nLab frame field

Definition

A frame field is locally a section of a frame bundle (of a manifold), hence a collection of vector fields that form a basis of the tangent space at each point.

Related concepts

• vielbein

• G-structure

• vector field

References

On submanifolds of Euclidean space via (the algebraic geometry of) their higher-dimensional coframe fields:

• Phillip Griffiths, Joseph Harris, Algebraic geometry and local differential geometry, Annales scientifiques de l’École Normale Supérieure, Serie 4, Volume 12 no. 3 (1979) 355-452 [numdam:ASENS_1979_4_12_3_355_0]

In the context of first-order formulation of gravity:

• Pietro Fré, §3.2.5 in: Gravity, a Geometrical Course, Volume 1: Development of the Theory and Basic Physical Applications, Spinger (2013) [doi:10.1007/978-94-007-5361-7]

  (on the historical origin of Cartan moving frames in Cartan geometry)

• Kirill Krasnov, §3 in: Formulations of General Relativity, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2020) [doi:10.1017/9781108674652, taster:pdf]