I'm trying to understand the paper:
"Isometric deformations of mixed type surfaces in Lorentz-Minkowski space" by A. Honda.
Specifically I am trying to understand:
Why does Honda embed four mixed type surfaces and arrange them so that they intersect like that? (page 4, figure 2)
Trying to grasp the concept of a "type-changing metric."
From what I understand you take a surface $S$ embedded in $\Bbb L^3$ which may have a positive definite induced metric, an indefinite induced metric, or a degenerate metric.
And then a mixed type surface would be classified by nonempty light like or space like regions from what I gathered.
My conceptual understanding so far is that you have this metric of some maximal or minimal Lorentz surface which may have singular points, curves, or higher dim. analogues.