(1,2)-Null Bertrand Curves in Minkowski Spacetime

2011/01/31 by Göçmen, Mehmet, Keleş, Sadık
#53A04 #53B30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.5935

Abstract

In this paper we study null Bertrand curves in R₁⁴ under the assumption the curve has a Cartan frame. We show that if the derivative vectors of the null Cartan curve in R₁⁴ is linearly independent, then this curve is not a Bertrand curve. Since then the already known notion of null Bertrand curves in R₁⁴ occurs only if the derivative vectors of the curve is linearly dependent. We will introduce an idea of Bertrand curves and abiding by this idea we bring to light under which conditions a null Cartan curve in R₁⁴ is a Bertrand curve.

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