For torsion-free connections with vectorial nonmetricity, necessary and sufficient conditions are derived for Finsler metrizability, with explicit Lagrangian construction when the conditions hold.
The Finsler Spacetime Condition for (α,β)-Metrics and Their Isometries.Universe, 9(4):198
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On the Finsler variational nature of autoparallels in metric-affine geometry
For torsion-free connections with vectorial nonmetricity, necessary and sufficient conditions are derived for Finsler metrizability, with explicit Lagrangian construction when the conditions hold.