Title: Curvature Dependent Energy of Surface Curves in Minkowski Space
Author(s): Talat Korpınar, Rıdvan Cem Demirkol, Vedat Asil
Pages: 254-263
Cite as:
Talat Korpınar, Rıdvan Cem Demirkol, Vedat Asil, Curvature Dependent Energy of Surface Curves in Minkowski Space, Int. J. Anal. Appl., 16 (2) (2018), 254-263.

Abstract


In this paper, we firstly introduce kinematics properties of the moving particle lying on a surface S. We assume that the particle corresponds to a different type of surface curves such that they are characterized by using the Darboux vector field W in Minkowski spacetime. Based on this result, we present geometrical understanding of the energy of the particle in each Darboux vector fields whether they lie on a spacelike surface or a timelike surface. Then, we also determine the bending elastic energy functional for the same particle on a surface S by assuming the particle has a bending feature of elastica. Finally, we prove that bending energy formula can be represented by the energy of the particle in each Darboux vector field W.

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