Spacelike elastic biharmonic curves with timelike \(M_1\) according to Bishop frame in Minkowski 3-space (Q2889983)

The authors study space-like curves in Minkowski 3-space which are elastic (of minimal total squared curvature when subjected to length and first order boundary data constraints), biharmonic (their parametrization \(\gamma\) satisfies \(\Delta^2\gamma = 0\)), and admit a time-like second basis vector \({\mathbf M}_1\) in a Bishop (or parallel transport) frame.NEWLINENEWLINEThe property of being a biharmonic curve can then be expressed in terms of the Bishop curvatures \(k_1\), \(k_2\) and their derivatives. The property of being a biharmonic elastica leads to relations between the Bishop frame vectors, the Bishop curvatures and curvature derivatives, a pointwise Lagrange multiplier, and a constant of integration.