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

Affiliation(s)

Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt.

Mathematics Department, Girls College of Science, University of Dammam, Dammam, KSA.

Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt.

Mathematics Department, Girls College of Science, University of Dammam, Dammam, KSA.

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 *R*^{2} are
given and plotted.

Cite this paper

Abdel-All, N. , Mohamed, S. and Al-Dossary, M. (2014) Evolution of Generalized Space Curve as a Function of Its Local Geometry.*Applied Mathematics*, **5**, 2381-2392. doi: 10.4236/am.2014.515230.

Abdel-All, N. , Mohamed, S. and Al-Dossary, M. (2014) Evolution of Generalized Space Curve as a Function of Its Local Geometry.

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