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This article is cited in 5 scientific papers (total in 5 papers)
Maximally Movable Riemannian Spaces with Torsion
V. I. Panzhenskij Penza State Pedagogical University
Abstract:
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, group of motions, Levi-Cività connection, metric connection, torsion tensor, Killing equations.
Received: 17.04.2008
Citation:
V. I. Panzhenskij, “Maximally Movable Riemannian Spaces with Torsion”, Mat. Zametki, 85:5 (2009), 754–757; Math. Notes, 85:5 (2009), 720–723
Linking options:
https://www.mathnet.ru/eng/mzm4730https://doi.org/10.4213/mzm4730 https://www.mathnet.ru/eng/mzm/v85/i5/p754
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