Curves in Lightlike Planes in Three-Dimensional Lorentz–Minkowski Space

Abstract

In this paper, we analyze the intrinsic geometry of lightlike planes in the three-dimensional Lorentz–Minkowski space M3. We connect the theory of curves lying in lightlike planes in M3 with the theory of curves in the simply isotropic plane I2. Based on these relations, we characterize some special classes of curves that lie in lightlike planes in M3.

Keywords

• Lorentz–Minkowski space
• pseudo-null curve
• pseudo-torsion
• isotropic curvature
• lightlike plane