Geodesic
Spaces of Finslerian type close to Riemannian spaces
Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 121-128

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Many special Finslerian metrics are constructed on the base of Riemmanian metrics (see, e.g., [1], [2]). In the present paper, using decomposition of metric tensor in Taylor series, we construct metrics of Finslerian type, which are close to Riemmanian metrics. 
@article{KUTGS_2003_24_a11,
     author = {V. I. Panzhenskij and M. V. Sorokina},
     title = {Spaces of {Finslerian} type close to {Riemannian} spaces},
     journal = {Trudy Geometricheskogo Seminara},
     pages = {121--128},
     publisher = {mathdoc},
     volume = {24},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a11/}
}
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V. I. Panzhenskij; M. V. Sorokina. Spaces of Finslerian type close to Riemannian spaces. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 121-128. http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a11/