Abstract
For the canonical almost-geodesic mapping π2 (e = 0), we prove an analog of the Beltrami theorem in the theory of geodesic mappings. We introduce canonical π2-flat spaces and obtain metrics for them in a special coordinate system.
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REFERENCES
N. S. Sinyukov, Geodesic Mappings of Riemannian Spaces [in Russian], Nauka, Moscow (1979).
J. Mikeš,“Geodesic mappings of affine connected and Riemannian spaces,” in: VINITI Series in Contemporary Mathematics and Its Applications. Thematic Surveys: Geometry [in Russian], Vol. 11, No.2, VINITI, Moscow (1994).
M. Shiha, Geodesic and Holomorphically Projective Mappings of Parabolic Kählerian Spaces [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Moscow (1993).
T. Thomas, “On the projective and equiprojective of paths,” Proc. Nat. Acad. Sci., 11, 198–203 (1925).
H. Weyl, “Zur infinitesimal geometrie Einordnung der projektiven und der Konformen Auffassung,” Götting. Nachr., 99–119 (1921).
E. Beltrami, “Teoria fondamental degli spazii di curvatura costante,” Ann. Mat., 2, No. 2, 232–255 (1902).
P. A. Shirokov, Selected Works on Geometry [in Russian], Kazan University, Kazan (1966).
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Hryhor'eva, T.I. Invariant Geometric Objects of the Canonical Almost-Geodesic Mapping π2 (e = 0). Ukrainian Mathematical Journal 54, 1602–1610 (2002). https://doi.org/10.1023/A:1023724001818
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DOI: https://doi.org/10.1023/A:1023724001818