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Automorphisms of spacetime manifold with torsion. (English) Zbl 1365.53023

Summary: In this paper we prove that the maximum dimension of the Lie group of automorphisms of the Riemann-Cartan \(4\)-dimensional manifold does not exceed 8, and if the Cartan connection is skew-symmetric or semisymmetric, the maximum dimension is equal to \(7\). In addition, in the case of the Riemann-Cartan \(n\)-dimensional manifolds with semisymmetric connection the maximum dimension of the Lie group of automorphisms is equal to \(n(n-1)/2+1\) for any \(n>2\).

MSC:

53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B05 Linear and affine connections
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References:

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