On generalized null Mannheim curves in E24

Abstract

In the present paper, we introduce the notion of Cartan‐framed generalized null Mannheim curves in four‐dimensional semi‐Euclidean space with index 2, double-struckE24. We obtain the Cartan (or Frenet) frames and curvature functions of the generalized Mannheim mate curve by the help of curvature functions and Cartan frames of the generalized null Mannheim curve. We proved that there are no generalized null Mannheim curves with timelike principal normal N in double-struckE24. The related examples and their projected images are also given.