Abstract
Abstract
For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi–Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure; this property is known as Finsler (or Berwald–Finsler) metrizability. In the present paper, we clarify, for four-dimensional SO(3)-invariant, Berwald–Finsler metrizable connections, the issue of the existence of an affinely equivalent pseudo-Riemannian structure. In particular, we find all classes of
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O
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-invariant connections which are not Levi–Civita connections for any pseudo-Riemannian metric—hence, are non-metric in a conventional way—but can still be metrized by SO(3)-invariant Finsler functions. The implications for physics, together with some examples are briefly discussed.