We have introduced lightcone framed surfaces and lightcone framed curves as mixed type surfaces and mixed type curves with singular points, respectively. A more general notion of singular surfaces, called generalised lightcone framed surfaces, is introduced in this paper. The notion of generalised lightcone framed surfaces includes not only the notion of lightcone framed surfaces, but also the notion of one-parameter families of lightcone framed curves at least locally. We investigate properties of generalised lightcone framed surfaces.
Masatomo Takahashi (Sat,) studied this question.