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Article
Differential Geometry of Moving Surfaces and its Relations to Solitons
Journal of Geometry and Symmetry in Physics (2011)
  • Andrei Ludu, Embry Riddle Aeronautical University
Abstract
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.
Keywords
  • differential geometry,
  • moving surface,
  • Cartan connection,
  • integrable forms,
  • moving frames,
  • Serret-Frenet,
  • Gauss-Weingarten
Disciplines
Publication Date
2011
Citation Information
Andrei Ludu. "Differential Geometry of Moving Surfaces and its Relations to Solitons" Journal of Geometry and Symmetry in Physics Vol. 21 (2011)
Available at: http://works.bepress.com/andrei_ludu/12/