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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 4, Pages 85–89 (Mi ivm1272)  
Brief communications

A Weyl-geodesic field of cones in a three-dimensional Riemannian space. II. First integrals of geodesics

O. S. Germanov

Nizhny Novgorod State Pedagogical University
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Abstract: 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.
Received: 17.05.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 4, Pages 76–80
DOI: https://doi.org/10.3103/S1066369X08040099
Bibliographic databases:
Document Type: Article
UDC: 514.764
Language: Russian
Citation: O. S. Germanov, “A Weyl-geodesic field of cones in a three-dimensional Riemannian space. II. First integrals of geodesics”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 4, 85–89; Russian Math. (Iz. VUZ), 52:4 (2008), 76–80
Citation in format AMSBIB
\Bibitem{Ger08}
\by O.~S.~Germanov
\paper A Weyl-geodesic field of cones in a three-dimensional Riemannian space. II. First integrals of geodesics
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 4
\pages 85--89
\mathnet{http://mi.mathnet.ru/ivm1272}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2445176}
\zmath{https://zbmath.org/?q=an:1173.53017}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 4
\pages 76--80
\crossref{https://doi.org/10.3103/S1066369X08040099}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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