Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hyperbolic Distance and double Cross Ratio.

  1. Jul 19, 2008 #1


    User Avatar
    Gold Member

    The question is as follows (by the way I'm asking here, cause the calculus and beyond forum seems to be primarily concerned with Calculus,DE, LA and AA):
    let f(z)=(2z+1)/(z+1) be an isometry of the hyperbolic plane H={z| Im(z)>0}.
    let l be a hyperbolic line in H which is invariatn under f, calculate the hyperbolic distance:
    p(z,f(z)) for some z in l.

    Now I want to use here the definition of the hyperbolic distance given by the cross ratio.

    So I found the fixed points of f, which are: w=(1+-(sqrt(5))/2, those points are in l (or so I think), from here we can use the cross ration definition, i.e:
    p(z,f(z))=[tex]log(D(w_1,z,f(z),w_2)[/tex] where D is the double cross ration defined by:
    from here just plug and go, but is my appraoch correct?

    thanks in advance.
  2. jcsd
  3. Jul 20, 2008 #2


    User Avatar
    Gold Member

    Can someone please hekp me with my questions in the three threads I've opened in the general math forum?

    The exam is on thursday, and I need as much help as I can have.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook