Proceedings of the International Conference on Geometry, Integrability and Quantization

Differential Geometry of Moving Surfaces and Its Relation to Solitons

Andrei Ludu

Abstract

In this article we present an introduction in the geometrical theory of motion of curves and surfaces in $\mathbb{R}^3$, and its relations with the nonlinear integrable systems. The working frame is the Cartan's theory of moving frames together with Cartan connection. The formalism for the motion of curves is constructed in the Serret-Frenet frames as elements of the bundle of adapted frames. The motion of surfaces is investigated in the Gauss-Weingarten frame. We present the relations between types of motions and nonlinear equations and their soliton solutions.

Article information

Source
Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2011), 43-69

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815615

Digital Object Identifier
doi:10.7546/giq-12-2011-43-69

Mathematical Reviews number (MathSciNet)
MR2856233

Zentralblatt MATH identifier
1382.37078

Citation

Ludu, Andrei. Differential Geometry of Moving Surfaces and Its Relation to Solitons. Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization, 43--69, Avangard Prima, Sofia, Bulgaria, 2011. doi:10.7546/giq-12-2011-43-69. https://projecteuclid.org/euclid.pgiq/1436815615


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