We investigate the problem of reconstruction of the variation of the metric tensor of a surface on the basis of a given variation of Christoffel symbols of the second kind under infinitesimal deformations of surfaces in the Euclidean space E 3.
Similar content being viewed by others
References
V. F. Kagan, Foundations of the Theory of Surfaces in Tensor Representation [in Russian], Part 2, OGIZ, Moscow (1948).
P. I. Petrov, “Main problems on non-Riemann geometry in a binary domain,” Dokl. Akad. Nauk SSSR, 140, No. 4, 768–769 (1961).
L. P. Eisenhart and O. Veblen, Proc. Nat. Acad. USA, 8, No. 2 (1922).
L. L. Bezkorovaina, Infinitesimal Areal Deformations and Equilibrium States of an Elastic Shell [in Ukrainian], AstroPrynt, Odessa (1999).
N. V. Efimov, “Qualitative problems in the theory of deformation of surfaces,” Usp. Mat. Nauk, 3, Issue 2 (24), 47–158 (1948).
V. F. Kagan, Foundations of the Theory of Surfaces in Tensor Representation [in Russian], Part 1, OGIZ, Moscow (1947).
N. S. Sinyukov, Geodesic Mappings of Riemann Spaces [in Russian], Nauka, Moscow (1979).
V. T. Fomenko, “On the unique determination of closed surfaces with respect to geodesic mappings,” Dokl. Akad. Nauk, 407, No. 4, 453–456 (2006).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 523–530, April, 2011.
Rights and permissions
About this article
Cite this article
Potapenko, I.V. On the reconstruction of the variation of the metric tensor of a surface on the basis of a given variation of christoffel symbols of the second kind under infinitesimal deformations of surfaces in the euclidean space E 3 . Ukr Math J 63, 609–616 (2011). https://doi.org/10.1007/s11253-011-0528-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-011-0528-6