Geodesic
Maximally Movable Riemannian Spaces with Torsion
Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 754-757 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that, among all Riemannian spaces of constant curvature, only three-dimensional spaces have torsion which is invariant under the group of motions. The torsion tensor in these spaces is covariantly constant and determines the torsion form. The ratio of the integral of this form over a bounded domain to its volume is a constant determining the torsion of the space. We introduce the notions of volume torsion and scalar torsion.
Keywords: Riemannian space, curvature, metric connection, Killing equations.
Mots-clés : group of motions, Levi-Cività connection, torsion tensor 
@article{MZM_2009_85_5_a10,
     author = {V. I. Panzhenskij},
     title = {Maximally {Movable} {Riemannian} {Spaces} with {Torsion}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {754--757},
     year = {2009},
     volume = {85},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a10/}
}
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V. I. Panzhenskij. Maximally Movable Riemannian Spaces with Torsion. Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 754-757. http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a10/

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