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The Bishop frame of the spacelike curve with a spacelike binormal in Minkowski 3-space. (English) Zbl 1216.83002
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.
MSC:
83A05Special relativity
53B30Lorentz metrics, indefinite metrics
51B20Minkowski geometries
83C10Equations of motion