## 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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