Abstract
This paper is concerned with the problem of finding a multiplier matrixg which converts a prescribed system of second-order ordinary differential equations to the Euler-Lagrange form. Sufficient conditions for the existence of a multiplier matrix are given in the form of an infinite system of linear algebraic equations, provided the entries ofg may be regarded as components of a (0, 2) symmetric tensor field. As an application, conditions for the local existence of a metric tensor compatible with a given torsion-free connection are deduced.
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Caviglia, G. Helmholtz conditions, covariance, and invariance identities. Int J Theor Phys 24, 377–390 (1985). https://doi.org/10.1007/BF00670805
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DOI: https://doi.org/10.1007/BF00670805