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Daytona Beach


Department of Mathematics

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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



Bulgarian Academy of Sciences

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.