Courant algebroid

concept in differential geometry

Thing general Q5178094

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Courant algebroid

Summary

Key Facts

Theodore James Courant is named after Courant algebroid^[1].
Courant algebroid is a type of vector bundle^[2].
Courant algebroid's underlying structure is recorded as vector bundle^[3].

Body

Definition and Type

Courant algebroid is a type of vector bundle^[2].

Origins

Theodore James Courant is named after Courant algebroid^[1].

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Quick Facts

Subclass of vector bundle

Properties

Defining formula \begin{align}{}[\phi ,[\chi ,\psi ]]&=[[\phi ,\chi ],\psi ]+[\chi ,[\phi ,\psi ]]\\{}[\phi ,f\psi]&=\rho (\phi )f\psi +f[\phi ,\psi]\\{}[\phi ,\phi ]&=\frac12D\langle \phi ,\phi \rangle\\{}\rho (\phi )\langle \psi ,\psi \rangle&=2\langle [\phi ,\psi ],\psi \rangle\end{align}

Imported from wholeness_audit_2026-05-02

Named after Theodore James Courant

Underlying structure(s) vector bundle

External References (3)

Freebase id /m/02q23sf

Microsoft academic id (discontinued) 2780623195

Nlab id Courant algebroid

🌐 Available in 3 languages

enCourant algebroid eoAlĝebroido de Courant ko쿠런트 준대수

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APA

4ort.xyz Knowledge Graph. (2026). Courant algebroid. Retrieved May 7, 2026, from https://4ort.xyz/entity/courant-algebroid

MLA “Courant algebroid.” 4ort.xyz Knowledge Graph, 4ort.xyz, 7 May. 2026, https://4ort.xyz/entity/courant-algebroid.

BibTeX

@misc{4ortxyz_courant-algebroid_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Courant algebroid}}, year = {2026}, url = {https://4ort.xyz/entity/courant-algebroid}, note = {Accessed: 2026-05-07}}

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According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Courant algebroid — https://4ort.xyz/entity/courant-algebroid (retrieved 2026-05-07)

Canonical URL: https://4ort.xyz/entity/courant-algebroid · Last refreshed: May 7, 2026