On Generalized Spacelike Mannheim Curves in Minkowski Space–Time

Null Darboux Curve Pairs in Minkowski 3-Space

“…Taking Euclidean 3-space as an example, a Bertrand curve shares its normal line with another curve and its curvature κ, torsion τ satisfy λκ + µτ = 1 for some constants λ and µ [1]; the principal normal line of a Mannheim curve coincides with the binormal line of another curve and its curvature κ, torsion τ satisfy κ = λ(κ 2 + τ 2 ) for some constant λ [2]. Over years, many mathematicians extended the notions of curve pairs, such as Bertrand curve, Mannheim curve, evolute and involute and so on from Euclidean space to Lorentz-Minkowski space [3][4][5].…”

On generalized null Mannheim curves in E24

“…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 …”