Boy's surface is an immersion of the real projective plane in $\Bbb R^3.$ And the real projective plane is a compactification of $\Bbb R^2$.
I've seen images of Boy's surface on the web. I'm interested in this from the context of pseudo-euclidean spaces. Specifically:
What does an immersion of conformally compactified Minkowski $(1+1)$ space into $\mathbf L^3$ look like?
Here $\mathbf L^3$ is Lorentz-Minkowski 3-space of signature $(++-).$