Geodesic
Dynamical systems on a~Riemannian manifold that admit normal shift
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 256-266

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Newtonian dynamical systems that accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor fields is constructed. 
@article{TMF_1995_103_2_a5,
     author = {A. Yu. Boldin and V. V. Dmitrieva and S. S. Safin and R. A. Sharipov},
     title = {Dynamical systems on {a~Riemannian} manifold that admit normal shift},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {256--266},
     publisher = {mathdoc},
     volume = {103},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a5/}
}
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A. Yu. Boldin; V. V. Dmitrieva; S. S. Safin; R. A. Sharipov. Dynamical systems on a~Riemannian manifold that admit normal shift. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 256-266. http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a5/