Bukcu, Bahaddin; Karacan, Murat Kemal The Bishop frame of the spacelike curve with a spacelike binormal in Minkowski 3-space. (English) Zbl 1216.83002 Selçuk J. Appl. Math. 11, No. 1, 15-25 (2010). The authors examine other than the well known Frénet frames of a 3-times continuously differentiable non-degenerate space-like curve with a space-like binormal invariant in semi-euclidean space. The authors generalize for a space-like curve with a space-like binormal [studied previously by L. R. Bishop, Am. Math. Mon. 82, 246–251 (1975; Zbl 0298.53001)] for three-dimensional Minkowski space-time. The Darboux vector (matrix) for a space-like curve with a space-like binormal was found. Using the derivative of the tangent vector \(T\) of the space-like curve with a space-like binormal, the relations between the curvature functions were found. Reviewer: Alex Gaina (Chisinau) Cited in 9 Documents MSC: 83A05 Special relativity 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 51B20 Minkowski geometries in nonlinear incidence geometry 83C10 Equations of motion in general relativity and gravitational theory Keywords:Bishop frame; adapted frame; space-like curve; Minkowski 3-space; Frénet frame Citations:Zbl 0298.53001 PDFBibTeX XMLCite \textit{B. Bukcu} and \textit{M. K. Karacan}, Selçuk J. Appl. Math. 11, No. 1, 15--25 (2010; Zbl 1216.83002)