Special Issue: Variational Principles and Conservation Laws in General RelativityNo Access

The metrizability problem for Lorentz-invariant affine connections

Department of Mathematics and Descriptive Geometry, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic

E-mail Address: [email protected]

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and

Jana Volná

Department of Mathematics and Descriptive Geometry, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219887816501103Cited by:0 (Source: Crossref)

Abstract

The invariant metrizability problem for affine connections on a manifold, formulated by Tanaka and Krupka for connected Lie groups actions, is considered in the particular cases of Lorentz and Poincaré (inhomogeneous Lorentz) groups. Conditions under which an affine connection on the open submanifold $ℝ \times (ℝ^{3} \ {(0, 0, 0)})$ of the Euclidean space $ℝ^{4}$ coincides with the Levi-Civita connection of some $SO (3, 1)$ , respectively $(ℝ^{4} \times_{s} SO (3, 1))$ -invariant metric field are studied. We give complete description of metrizable Lorentz-invariant connections. Explicit solutions (metric fields) of the invariant metrizability equations are found and their properties are discussed.

Keywords:

AMSC: 53B05, 53A55, 58D19, 22E43

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