We establish a condition for two symmetric tensor fields that is necessary and sufficient for the existence of a displacement vector in the case of infinitesimal deformation of a surface in the Euclidean space E 3.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. J. Bonnet, “Mémoire sur la théorie des surfaces applicables sur une surface donée,” J. École Polytechnique, 25, 1–51 (1867).
L. L. Bezkorovaina, Areal Infinitesimal Deformations and Equilibrium States of an Elastic Shell [in Ukrainian], AstroPrynt, Odessa (1999).
S. G. Leiko and Yu. S. Fedchenko, “Infinitesimal rotary deformations of surfaces and their application to the theory of elastic shells,” Ukr. Mat. Zh., 55, No. 12, 1697–1703 (2003).
V. T. Fomenko, “ARG-deformations of a hypersurface with a boundary in Riemannian space,” Tensor, 54, 28–34 (1993).
E. V. Ferapontov, “Surfaces in 3-spaces possessing nontrivial deformations which preserve the shape operator,” in: Differential Geometry and Integrable Systems in Differential Geometry (Tokyo, July 17–21, 2001), American Mathematical Society, Providence (2002), pp. 145–159.
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 2, pp. 199–202, February, 2010.
Rights and permissions
About this article
Cite this article
Potapenko, I.V. New equations of infinitesimal deformations of surfaces in E 3 . Ukr Math J 62, 222–226 (2010). https://doi.org/10.1007/s11253-010-0346-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-010-0346-2