On generalized partially null Mannheim curves in Minkowski space-time

Abstract

In this paper we define generalized partially null and pseudo null Mannheim curves in Minkowski space-time E 4 1. We prove that there are no non-geodesic generalized partially null Mannheim curves in E 4 1 , by considering the cases when the corresponding mate curve is a spacelike, a timelike, null Cartan, partially null or pseudo null Frenet curve. We also answer the question: "Can a partially null Frenet curve be generalized mate curve of the generalized pseudo null Mannheim curve in Minkowski space-time?"

On generalized null Mannheim curves in E24

“…Also, they prove that there are no generalized null Mannheim curves whose generalized Mannheim mate curve is a pseudo null curve. In addition, generalized spacelike Mannheim curves and generalized timelike Mannheim curves are studied in Akyiğit et al, Ersoy et al, and Uçum et al 15–17 Pseudo null and partially null Mannheim curves are examined in Nešović and Grbović 18 . The generalized spacelike Mannheim curves in Minkowski space–time, the Frenet frame of which contains only non‐null vectors, are characterized in İlarslan et al 19 …”

“…In addition, generalized spacelike Mannheim curves and generalized timelike Mannheim curves are studied in Akyigit et al, Ersoy et al, and Uçum et al [15][16][17] Pseudo null and partially null Mannheim curves are examined in Nešović and Grbović. 18 The generalized spacelike Mannheim curves in Minkowski space-time, the Frenet frame of which contains only non-null vectors, are characterized inİlarslan et al 19 In the present paper, we define the generalized null Mannheim curves in four-dimensional semi-Euclidean space with index 2, E 4 2 , by taking consideration of the principal normal vector N of the generalized lightlike Mannheim curve fully lies in the lightlike plane spanned by the vectors B * 1 and B * 2 of the Mannheim mate curve. We also characterize these curves and their generalized Mannheim mate curves in terms of their curvature functions and obtain relations between their frames.…”