A Weyl-geodesic field of cones in a three-dimensional Riemannian space. II: First integrals of geodesics (Q1006962)

First integrals of second order for differential equations of geodesics in three dimensional Riemannian and Weyl spaces are constructed. Based on his previous paper [Russ. Math. 48, No. 5, 22--29 (2004); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 48, No. 5, 24--32 (2004; Zbl 1093.53036)], the author finds seven types of three dimensional Riemannian spaces whose equations of geodesics admit a quadratic first integral generated by a special geodesic field of cones. These types are separated in two distinct sets (of three and four types respectively) according to some technical properties.