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Projective structures in Sinyukov manifolds. (English) Zbl 0795.53018
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 263-271 (1992).
The author studies geodesic mappings on Sinyukov manifolds, i.e. in Sinyukov’s terms \(L_ n\)-spaces satisfying the following conditions: \(R_{ij,k} = a_ kg_{ij} + b_ i g_{jk} + b_ i g_{ik}\) where \(R_{ij}\) and \(g_{ij}\) denote Ricci and metric tensors, \(a_ k,b_ k\) are covectors. If an Einstein space admits geodesic mappings then it corresponds to a certain Sinyukov manifold.
For the entire collection see [Zbl 0764.00002].
Reviewer: J.Mikeš (Odessa)
53B20 Local Riemannian geometry