Degenerate curves in pseudo-Euclidean spaces of index two. (English) Zbl 1020.53005

Ferrández, Angel; Giménez, Angel; Lucas, Pascual

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 3rd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 14-23, 2001. Sofia: Coral Press Scientific Publishing. 209-223 (2002).

Along a curve in a Euclidean space, parametrization by arc-length allows to define unique curvature functions with the help of the standard Frenet-reference-frame construction. In the paper under review the authors investigate to what extent this method carries over to degenerate curves in pseudo-Euclidean spaces of index two. To that end, a certain “pseudo-arc-length” parametrization is used. Among other things, a congruence theorem for degenerate curves is presented, and some examples in low dimensions are worked out.
For the entire collection see [Zbl 0980.00035].

Reviewer: Volker Perlick (Berlin)

MSC:

53A35	Non-Euclidean differential geometry
53A04	Curves in Euclidean and related spaces

Keywords:

degenerate curves; pseudo-Euclidean space; pseudo-arc-length; congruence