Abstract
The Lagrangian density for formulating the Finslerian gravitational field equations is constructed by replacing the tangent vectors entering a direction-dependent density by the auxiliary vector field. The Lagrangian derivative is represented in terms of the tensor densities associated with an initial direction-dependent density. A particular case, where the direction-dependent density is chosen in the form of the contraction of the FinslerianK-tensor of curvature multiplied by the Jacobian, is treated in detail.
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Asanov, G.S. Variational principle for the Finslerian extension of general relativity. Aeq. Math. 24, 207–229 (1982). https://doi.org/10.1007/BF02193045
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DOI: https://doi.org/10.1007/BF02193045