In mathematics, a coframe or coframe field on a smooth manifold is a system of one-forms or covectors which form a basis of the cotangent bundle at every point.[1] In the exterior algebra of , one has a natural map from , given by . If is dimensional, a coframe is given by a section of such that . The inverse image under of the complement of the zero section of forms a principal bundle over , which is called the coframe bundle.
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Differential Geometry: Lecture 8: coframes and structure equations for R3
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Differential Geometry: Lecture 20 part 2: Gauss' Awesome Theorem
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Differential Geometry: Lecture 18: adapted frame fields of surfaces in R3
Transcription
References
- Manuel Tecchiolli (2019). "On the Mathematics of Coframe Formalism and Einstein-Cartan Theory -- A Brief Review". Universe. 5(10) (Torsion Gravity): 206. arXiv:2008.08314. Bibcode:2019Univ....5..206T. doi:10.3390/universe5100206.
See also
- ^ "Structure coefficients of a coframe". Mathematics Stack Exchange. Retrieved 2024-01-19.