Characterizations of a Bertrand Curve According to Darboux Vector

Abstract

In this paper, we first take a Bertrand curve pair and then we use Darboux vector instead of mean curvature vector to give characterizations of Bertrand partner curve by means of the Bertrand curve. By making use of the relations between the Frenet frames of the Bertrand curve pair we give the differential equations and sufficient conditions of harmonicity(biharmonic or 1-type harmonic) of the Bertrand partner curve in terms of the Darboux vector of the Bertrand curve. After driving the conclusions we write an example to demonstrate how our assumptions come true

Keywords

• Bertrand curve pair
• differential equation,
• biharmonic curve,
• Laplace operator

References

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