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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.

53C22 Geodesics in global differential geometry
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)