I have a question abourt some calculus in an article, I found it in the internet but I didn't understood some steps. his is the link of the article;
http://arxiv.org/abs/math/0311352
In the first paragraph of page 19 the author says :
Let
;)Hn+1 be an orientable (n;)1)-dimensional compact submanifold in a geodesic sphere S of Hn+1 of center a in Hn+1 and geodesic radius r, and let :Mn;)Hn+1 be an orientable compact hypersurface with boundary =;)(;)M).Consider the vector field in Hn+1 represented in this model as Y(p) =;)a;)g(a,p) wher g is the metric define on H n+1.for every p;)Hn+1. Observe that Y is a conformal vector field in Hn+1 which is orthogonal to the geodesic spheres centered at the point a, with (p) =g(a,p)=cosh(distance(a,p)))and|Y(p)|= sinh(distance(a,p)),for every p;) of Hn+1.Therefore, along the sphere S we have Y= sinh;);).
I don't understand why (a,p)=cosh(distance(a,p))) and |Y(p)|= sinh(distance(a,p)).
Please help me because I will presnet this work in my class next week and I have no idea about the detail of calculus