Using the mathematical MAPLE package, we construct models of surfaces of revolution of constant Gaussian curvature and geodesic lines on such surfaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. V. Alekseevskij, E. B. Vingerg, and A. S. Solodovnikov, “Geometry of spaces of constant curvature,” Encycl. Math. Sci. 29, 1–138 (1993).
J. A. Wolf, Spaces of Constant Curvature, Am. Math. Soc., Providence, RI (2011).
D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen. 2 Aufl. [in German], Lect. Notes Math. 55, Springer, Berlin etc. (1975).
S. N. Krivoshapko, V. N. Ivanov, and S. M. Khalabi, Analytic Surfaces [in Russian], Nauka, Moscow (2006).
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vol. II, John Wiley and Sons, New York etc. (1969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 18, No. 3, 2018, pp. 64-74.
Rights and permissions
About this article
Cite this article
Cheshkova, M.A. Construction of Geodesics on Surfaces of Revolution of Constant Gaussian Curvature. J Math Sci 253, 360–368 (2021). https://doi.org/10.1007/s10958-021-05234-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-021-05234-4