Description
Autoparallel curves in metric-affine geometries are generally non-variational and do not generally coincide with the Euler-Lagrange equations of any Lagrangian. For symmetric connections with vectorial nonmetricity, we show that the autoparallel equations can be realized as geodesics of a suitably chosen Finsler metric, reducing the problem of variationality to Finsler metrizability. By formulating this as a first-order partial differential equation, we obtain necessary and sufficient conditions and classify all $(\alpha,\beta)$-metrics whose geodesics coincide with these autoparallels. For generalized $(\alpha,\beta)$-metrics, necessary conditions are obtained.
Author
Lehel Csillag
(Transilvania University Brasov)
Co-authors
Dr
Christian Pfeifer
(ZARM, Bremen)
Prof.
Nicoleta Voicu
(Transilvania University Brasov)
Prof.
Salah Elgendi
(Islamic University of Madinah)
