Abstract
We give a complete description of two-dimensional surfaces with flat normal connections in Riemannian spaces of constant curvature with geodesics having constant first curvature. In particular, we show that all such surfaces are of constant curvature.
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References
L. P. Eisenhart,Riemannian Geometry, Princeton (1926).
P. K. Rashevskii,Riemannian Geometry and Tensor Analysis [in Russian], Nauka, Moscow (1964).
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Translated fromMatermaticheskie Zametki, Vol. 68, No. 4, pp. 579–586, October, 2000.
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Fomenko, V.T. Two-dimensional surfaces with flat normal connections in spaces of constant curvature carrying geodesics of constant curvature. Math Notes 68, 496–501 (2000). https://doi.org/10.1007/BF02676730
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DOI: https://doi.org/10.1007/BF02676730