Fields of cones of second order and their induced connections. III: First integrals of geodesics (Q1357949)

[For part I, see Zbl 0611.53019. Part II has been deposited at the archives of VINITI under No. 2421--B90 (1990) and has not been reviewed.] The paper is devoted to constructions of Riemannian manifolds spaces such that the differential equations of geodesics admit a first integral of quadratic type as well as to a construction of Weyl spaces with differential equations of geodesics admitting a first integral of quadratic quotient form. The existence of a symmetric tensor having some interesting geometrical properties concerning its field of cones plays an essential role in these constructions.