Geodesic
Torsion and curvature for the $6$-commutator
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 49-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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Torsion and curvature for $6$-commutator on $Vect(2)$ are calculated. It is proved that $6$-curvature ($6$-torsion) can be presented as a exterior product of usual curvature (usual torsion) by some $4$-form.
Keywords: $N$-commutator, curvature, Bianchi identities.
Mots-clés : torsion 
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     author = {A. Dzhumadil'daev},
     title = {Torsion and curvature for the $6$-commutator},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {49--52},
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}
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A. Dzhumadil'daev. Torsion and curvature for the $6$-commutator. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 49-52. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a25/

[1] A. S. Dzhumadil'daev, “$N$-commutators”, Comment. Math. Helv., 79:3 (2004), 516–553 | DOI | MR

[2] S. P. Novikov, I. A. Taimanov, Modern Geometric Structures and Fields, Graduate Studies in Math., 71, AMS, 2006 | MR | Zbl