Abstract
In this paper, we first define the pseudo-circular evolute of a lightcone framed curve in the Lorentz–Minkowski 3-space, and show that the pseudo-circular evolute of a lightcone framed curve can be seen as a generalization of the circular evolute of a framed curve without type changing. We also define an involute of a lightcone framed curve, and study the duality relations between involutes and pseudo-circular evolutes. Moreover, we study the pseudo-circular evolutes and involutes with respect to a lightcone circle frame, and investigate the relationship with respect to a projection map. Meanwhile, examples are given for explaining the objects we investigated, which also show a certain physical significance of our investigation.
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