I can do all the questions apart from part iv). After some work, I got . Unfortunately, the image of this under the metric is not 1/im(z)^2 as it ought to be.

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- May 11th 2013, 03:16 AMPlato13An isometry between riemannian metric spaces
I can do all the questions apart from part iv). After some work, I got . Unfortunately, the image of this under the metric is not 1/im(z)^2 as it ought to be.

- May 11th 2013, 08:42 AMxxp9Re: An isometry between riemannian metric spaces
let ,

- May 11th 2013, 10:41 AMPlato13Re: An isometry between riemannian metric spaces
If you take the real part of what I got above, you get which disagrees with your answer due to the 3y^2 instead of y^2.

- May 11th 2013, 02:00 PMxxp9Re: An isometry between riemannian metric spaces
so you may need to check your calculation

- May 12th 2013, 08:00 AMPlato13Re: An isometry between riemannian metric spaces
Ok I've had another go. Can you tell me where I go wrong. Think of R^2 as C and let z=x+iy. Then, a(t)=z+t is a generating curve for e=(1,0).

so whose derivative is so that evaluating at t=0 gives which appears even further from the truth!. I think it hinges on what the derivative of is. My reasoning was which differentaing w.r.t t gives . Thanks - May 12th 2013, 08:29 AMPlato13Re: An isometry between riemannian metric spaces
Sorted it now thanks