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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.

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