Motion of surfaces in 3-dimensional space

Kazuaki Nakayama and Miki Wadati

Mathematics and Computers in Simulation (MATCOM), 1994, vol. 37, issue 4, 417-430

Abstract: Kinematics of surfaces in 3-dimensional space is formulated in terms of the differential geometry. The formulation is intrinsic and the surface is described by its metric and curvature tensors. It is found that the introduction of nontrivial time evolution of coordinate system makes the theory transparent. Applications to some surfaces, which are paremetrized by the lines of curvature, are presented. As a concrete example, 1-soliton solution of the zero-curvature surfaces is obtained.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:37:y:1994:i:4:p:417-430

DOI: 10.1016/0378-4754(94)00028-X

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