Report from the lectures September ¡­

Report from the lectures

September 27. and 28.

On Monday I defined the hyperbolic metric in H and proved that (apart from being a metric) it is satisfies the properties given in (d4) and (d5) (p. 26). Then I defined the homeomorphism G from D to D. On Tuesday I explained what we mean by a M?bius transformations in D and gave general formulas for these.Then I defined the hyperbolic metric in D and started to calculate formulas for this metric. I will proceed with this next week, and then proceed with chapter 8. (I will talk about the stuff in chapter 6, when I deduce the area formula for an hyperbolic triangle). I assigned the problems 2.9, 5.1 and 7.8 for next week.