given two points $x, y$ on an n-sphere (embedded in $\mathbb{R}^{n+1})$, their inner product $\langle x, y \rangle = x_1y_1 + \dots + x_{n+1}y_{n+1}$ will be a scalar in $[-1, 1]$ which can be interpreted as the cosine similarity between the two points.
What would be an equivalent measure for points in a hyperbolic space? The Minkowski inner product looks like a good starting point, but I have no idea how to properly convert it to a bounded similarity measure.
(sorry if the description isn't extremely formal, I hope I was clear enough)
Thanks