For torsion-free connections with vectorial nonmetricity, necessary and sufficient conditions are derived for Finsler metrizability, with explicit Lagrangian construction when the conditions hold.
Denoting: Λ∶=m q = c1 c3 , τ∶= p q ,(73) the differential constraint in (58) becomes precisely (44)
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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.