For torsion-free connections with vectorial nonmetricity, necessary and sufficient conditions are derived for Finsler metrizability, with explicit Lagrangian construction when the conditions hold.
Moreover, they give, up to the precise expression ofτ, the coordinate expressions of the differential constraints 2
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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.