Why are they called "screen" distributions?

Question

If $V$ is a vector space and $g$ is a symmetric degenerate bilinear form on $V$, every complementary subspace to the radical ${\rm rad}(V)$ is called a "screen subspace" of $V$: we have an orthogonal direct sum $V = {\rm rad}(V) \oplus SV$.

Likewise, if $M$ is a smooth manifold and $g$ is a symmetric and degenerate $(0,2)$-tensor field on $M$, any complementary distribution to ${\rm rad}(TM)$ is called a "screen distribution" of $M$: we have the orthogonal Whitney sum $TM = {\rm rad}(TM) \oplus S(TM)$.

These definitions are given by Bejancu and Duggal in several of their books and works. But I can't see any motivation for the name "screen".

Answer 1

Naturally, one should consider the quotient space $V/{\rm rad}(V)$ which consists of ${\rm rad}(V)$-rays (affine spaces parallel to ${\rm rad}(V)$). A screen space $SV$ intersects a ray in exactly one point, like a screen intersects the rays from a projector. Similarly on a manifold.

Answer 2

The word "screen" refers to lightlike dimensional reductions, a worldline in $(d+1)+1$ dimensional space-time is projected onto the screen $x^{d+1}=0$ and the projected $d+1$ dimensional curve is parameterized by Galilean time $t$. The projection is called the "shadow" on the "screen". For an introduction, see Classical aspects of lightlike dimensional reduction.

A particular feature of the dimensional reduction is that relativistic dynamics projects to non-relativistic physics on the screen. The history goes back to Eisenhart's Dynamical Trajectories and Geodesics (1929), who discovered the equivalence of relativistic Poincaré invariance and nonrelativistic Galilei invariance in a lightlike reduced spacetime with one dimension less.