s-Degenerate curves in Lorentzian space forms

✍ Scribed by Angel Ferrández; Angel Giménez; Pascual Lucas

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 131 KB
• Volume: 45
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00129-8

✦ Synopsis

In this paper we introduce s-degenerate curves in Lorentzian space forms as those ones whose derivative of order s is a null vector provided that s > 1 and all derivatives of order less than s are space-like (see the exact definition in Section 2). In this sense classical null curves are 1-degenerate curves. We obtain a reference along an s-degenerate curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space-time and it will be called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the s-degenerate helices (i.e. s-degenerate curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in dimension four.