Robinson, J.; Zund, J. D. A theorem on geodesic mappings. (English) Zbl 0164.22103 Tensor, New Ser. 19, 300-302 (1968). This paper proves that there does not exist a non-trivial geodesic mapping \[ \Gamma_{ij}^h \to \hat{\Gamma}_{ij}^h = \Gamma_{ij}^h+\delta_i^h\psi_j+\delta_j^h\psi_j,\quad \psi_i\ne 0 \] which takes a Riemannian \(V_n\) \((n>2)\) onto a \(\tilde V_n\), which is recurrent, but is not of constant curvature. Thus the celebrated Beltrami theorem of classical differential geometry does not admit nontrivial generalizations. The paper corrects and extends a previous result of N. S. Sinyukov [Dokl. Akad. Nauk SSSR, n. Ser. 98, 21–23 (1954; Zbl 0056.15301)]. Reviewer: J. Robinson Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 53-XX Differential geometry Keywords:differential geometry PDF BibTeX XML Cite \textit{J. Robinson} and \textit{J. D. Zund}, Tensor, New Ser. 19, 300--302 (1968; Zbl 0164.22103)