Singularity properties of spacelike curves in 3D Cahen–Wallach space

The propagation of gravitational waves in Cahen–Wallach space is intrinsically linked to the geometry of spacelike curves, whose singularities can lead to wavefront caustics and focusing. In this paper, we systematically investigate the singularity structure of spacelike curves in three-dimensional Cahen–Wallach space. By introducing height functions and employing singularity theory, we analyze the contact between the curve and associated geometric structures. We derive the geometric invariants and singularities associated with the tangent normal indicatrix and the tangent binormal indicatrix surfaces of spacelike curves. As an application, we give an example to explain the main results in this paper.