On projective properties of affinely connected spaces which admit absolute parallelism of vectors (Q1909842)

Let \(G_n\) denote an \(n\)-dimensional affinely connected manifold with torsion and let \(AG_n\) denote such a space which, in addition, admits absolute parallelism of vectors. In this paper, the author considers projective properties of \(G_n\) admitting \((n-1)\) independent linear-fractional integrals of geodesics (see also the author's earlier paper [\textit{Sh. A. Yafarov}, Itogi Nauki Tekh., Ser. Probl. Geom. 16, 127-153 (1984; Zbl 0565.53013)]). He gives examples of non-projectively Euclidean spaces \(G_n\) admitting such integrals. The author further expresses conditions under which an \(AG_n\) admits linear homogeneous integrals of geodesics of a specific type, and he elaborates on the question of existence of such spaces.