Re: [math-fun] Homotheties of the hyperbolic plane

On 2/13/08, Dan Asimov <dasimov@earthlink.net> wrote:

... But any bijection of a manifold that multiplies distance by a fixed constant c must be angle-preserving ...

Is that a theorem? I couldn't justify it, and that's why I resorted to the computation. Even then, I assumed that the transformation had a fixed point, and furthermore was isotropic at that point. Neither of these assumptions has currently been justified, however plausible they might seem. WFL