I have problems understanding vector addition in Hyperbolic space. In the Poincaré ball model, vector addition/translation is the Möbis addition and defined as:
$$ x \oplus_c y = \frac{(1+2c\langle x,y \rangle+c \lVert y \rVert^2)x+(1-c \lVert x \rVert^2)y}{1+2c \langle x,y \rangle+c^2 \lVert x \rVert^2 \lVert y \rVert^2}$$
with c being the curvature. I was wondering how a vector addition/translation is defined in the hyperboloid model? Unfortunately, I couldn't find an exact answer. I would really appreciate your help!
Thank you!!! :D