Geodesic
A Weyl-geodesic field of cones in a three-dimensional Riemannian space. II. First integrals of geodesics
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 85-89

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We study three-dimensional Riemannian spaces and Weyl spaces such that the geodesic equations admit a first integral of second order. With respect to a special coordinate system, we find objects which completely determine connection of these spaces as well as the integrals.
Keywords: first integral of differential equation, geodesic lines, cone of directions, geodesic field of directions, Riemannian space, Weyl space. 
@article{IVM_2008_4_a8,
     author = {O. S. Germanov},
     title = {A {Weyl-geodesic} field of cones in a three-dimensional {Riemannian} space. {II.} {First} integrals of geodesics},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {85--89},
     publisher = {mathdoc},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_4_a8/}
}
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O. S. Germanov. A Weyl-geodesic field of cones in a three-dimensional Riemannian space. II. First integrals of geodesics. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 85-89. http://geodesic.mathdoc.fr/item/IVM_2008_4_a8/