Proceedings of the International Conference on Geometry, Integrability and Quantization

Extremals of the Generalized Euler-Bernoulli Energy and Applications

Óscar J. Garay

Abstract

In this survey we describe a general method to deal with the variational problem associated to the generalized elastic curves, paying special attention to closed critical curves in real space forms due to its special geometric significance. We illustrate the method by studying particular choices of this energy in some more detail. Finally, we will review also some interesting applications of generalized elasticae to other higher dimensional variational problems in Physics, Biophysics and the Theory of Submanifolds.

Article information

Source
Proceedings of the Tenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2009), 56-87

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436793436

Digital Object Identifier
doi:10.7546/giq-10-2009-56-87

Mathematical Reviews number (MathSciNet)
MR2757826

Zentralblatt MATH identifier
1261.58008

Citation

Garay, Óscar J. Extremals of the Generalized Euler-Bernoulli Energy and Applications. Proceedings of the Tenth International Conference on Geometry, Integrability and Quantization, 56--87, Avangard Prima, Sofia, Bulgaria, 2009. doi:10.7546/giq-10-2009-56-87. https://projecteuclid.org/euclid.pgiq/1436793436


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