What is the generator of translation in the BeltramiKlein model of the hyperbolic plane?
closed as too localized by Ryan Budney, José FigueroaO'Farrill, Will Jagy, Richard Kent, Andy Putman Jun 3 '11 at 4:45This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


Hyperbolic plane is a homogeneous space $G/H$ where $G$ acts by isometries and so any reasonable defined `translation' is given by the natural left action of $G$. Decide what elements of $G$ will you call translations and then for any abstract generator $X\in\mathfrak{g}$ such that $\exp{tX}$ is translation, compose the natural left action with diffeomorphism of $G/H$ to your favorite model. Differentiate the resulting map at zero and you are done. If I am not mistaken, this question is more suitable for math.SE. 

