Mikeš, Josef Geodesic mappings onto semisymmetric spaces. (English. Russian original) Zbl 0835.53049 Russ. Math. 38, No. 2, 35-41 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 2 (381), 37-43 (1994). Geodesic mappings of Riemannian spaces onto semisymmetric equiaffine spaces and Riemannian spaces are studied.The author proves that compact semisymmetric Riemannian spaces of nonconstant curvature and non-Einsteinian Ricci-semisymmetric Riemannian spaces do not admit non-trivial global geodesic mappings. He finds new classes of equiaffine spaces which do not admit non-trivial geodesic mappings onto Riemannian spaces. Such spaces are determined, up to an affine transformation, by the configuration of their geodesic lines. Reviewer: Gh.Pitiş (Braşov) Cited in 1 Document MSC: 53C22 Geodesics in global differential geometry 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:geodesic map; semisymmetric space; equiaffine space; Riemannian space PDF BibTeX XML Cite \textit{J. Mikeš}, Russ. Math. 38, No. 2, 1 (1994; Zbl 0835.53049); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 2 (381), 37--43 (1994) OpenURL