Minimal curves of neutral space (Q2761517)

The four-dimensional neutral space \(E_{4,2}\) is a real point pseudo-Euclidean space. A curve \(\gamma\) in the neutral space is called a minimal curve if in each of its ordinary points the natural parameter of the curve is equal to zero. The authors give a characterization of some classes of plane and space minimal curves in terms of fundamental objects. For example, the following results are proved: NEWLINENEWLINENEWLINEThe plane minimal curve of the first class with zero absolute invariant \(\{\Lambda_1^1\}\) is an isotropic straight line of the neutral space \(E_{4,2}\). For spiral curves of general type in the neutral space \(E_{4,2}\) the main object is a fundamental object of the fourth order.