Geodesic
Newtonian normal shift in multidimensional Riemannian geometry
Sbornik. Mathematics, Tome 192 (2001) no. 6, pp. 895-932

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An explicit description of all Newtonian dynamical systems admitting normal shift in Riemannian manifolds of dimension $n\geqslant 3$ is obtained. On this basis the kinematics of the normal shift of hypersurfaces along trajectories of such dynamical systems is studied. 
@article{SM_2001_192_6_a6,
     author = {R. A. Sharipov},
     title = {Newtonian normal shift in multidimensional {Riemannian} geometry},
     journal = {Sbornik. Mathematics},
     pages = {895--932},
     publisher = {mathdoc},
     volume = {192},
     number = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_6_a6/}
}
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R. A. Sharipov. Newtonian normal shift in multidimensional Riemannian geometry. Sbornik. Mathematics, Tome 192 (2001) no. 6, pp. 895-932. http://geodesic.mathdoc.fr/item/SM_2001_192_6_a6/