Null Quaternionic Bertrand Partner Curves

Abstract

In this paper, we study null quaternionic Bertrand curves in the semi-Euclidean spaces \(E_{1}^{3}\) and \(E_{1}^{4}\), respectively. We obtain some characterizations for null quaternionic Bertrand partner curves. We show that the constant distance between the quaternionic partner curves is independent from the first curvatures of the curves in both spaces \(E_{1}^{3}\) and \(E_{1}^{4}\).