Skip to main content
Log in

Normal and tangential geodesic deformations of the surfaces of revolution

  • Published:
Ukrainian Mathematical Journal Aims and scope

We study special infinitesimal geodesic deformations of the surfaces of revolution in the Euclidean space E 3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. N. Vekua, Generalized Analytic Functions [in Russian], Nauka, Moscow (1988).

    MATH  Google Scholar 

  2. L. L. Bezkorovaina, Areal Infinitely Small Deformations and Steady States of Elastic Shells. A Manual [in Ukrainian], Astroprynt, Odessa (1999).

  3. E. D. Fesenko, “Infinitely small conformal deformations of closed surfaces of positive Gaussian curvature,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 3 (82) (1969).

  4. S. G. Leiko, “Infinitesimal rotation transformations and deformations of surfaces in a Euclidean space,” Dokl. Ros. Akad. Nauk, 344, No. 2, 162–164 (1994).

    MathSciNet  Google Scholar 

  5. N. S. Sinyukov and M. L. Gavril’chenko, “Infinitely small geodesic deformations of the surfaces,” in: Proc. of the Third Republ. Conf. of Belorussian Mathematician [in Russian], Minsk (1971).

  6. Zh. Radulovich, J. Mikeš, and M. L. Gavril’chenko, Geodesic Maps and Deformations of the Riemannian Spaces [in Russian], Odessa, Olomouts (1997).

    Google Scholar 

  7. V. T. Fomenko, “On the unique definition of closed surfaces with respect to geodesic maps,” Dokl. Akad. Nauk, 407, No. 4, 453–456 (2006).

    MathSciNet  Google Scholar 

  8. N. I. Kovantsov, Differential Geometry, Topology, and Tensor Analysis. A Collection of Problems [in Russian], Vyshcha Shkola Kiev (1989).

  9. S. H. Leiko and Yu. S. Fedchenko, “Vectors of displacements for conformal rotation deformations of the surfaces of revolution,” Visn. Odesa Univ., Ser. Fiz.-Mat. Nauk, 8, Issue 2, 50–54 (2003).

    MATH  Google Scholar 

  10. L. P. Eisenhart, Riemannian Geometry, Princeton, Princeton University (1926).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 10, pp. 1396–1402, October, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fedchenko, Y.S. Normal and tangential geodesic deformations of the surfaces of revolution. Ukr Math J 61, 1640–1648 (2009). https://doi.org/10.1007/s11253-010-0303-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-010-0303-0

Keywords

Navigation