Evolution of Generalized Space Curve as a Function of Its Local Geometry

Nassar H. Abdel-All, Samah G. Mohamed, Mariam T. Al-Dossary

Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt.
Mathematics Department, Girls College of Science, University of Dammam, Dammam, KSA.

DOI: 10.4236/am.2014.515230                

Abstract

Kinematics of moving generalized curves in a n-dimensional Euclidean space is formulated in terms of intrinsic geometries. The evolution equations of the orthonormal frame and higher curvatures are obtained. The integrability conditions for the evolutions are given. Finally, applications in R² are given and plotted.

Keywords

Inelastic Curve, Curve Flow, Evolution of Curves

Conflicts of Interest

The authors declare no conflicts of interest.

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