Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
2011
Abstract/Description
In this article we present an introduction in the geometrical theory of motion of curves and surfaces in R3, 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.
Publication Title
Journal of Geometry and Symmetry in Physics
DOI
https://doi.org/10.7546/jgsp-21-2011-1-28
Publisher
Bulgarian Academy of Sciences
Scholarly Commons Citation
Ludu, A. (2011). Differential Geometry of Moving Surfaces and Its Relation to Solitons. Journal of Geometry and Symmetry in Physics, 21(). https://doi.org/10.7546/jgsp-21-2011-1-28
Additional Information
Dr. Ludu was not affiliated with Embry-Riddle Aeronautical University at the time this articles was published.
Also presented at the 13th International Conference on Geometry, Integrability and Quantization, held June 3-8, 2011, in Varna, Bulgaria. Proceedings volume published in 2012 by Avangard Prima, pp. 43-49.