Important 4D spaces:
Simulate it. Just simulate it.
Video 1. 4D Toys: a box of four-dimensional toys by Miegakure (2017) Source.
The complex dot product is defined as:
E.g. in :
We can see therefore that this is a form, and a positive definite because:
Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.
with extra structure added to make it into a metric space.
Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.