- #1
chris_avfc
- 85
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Homework Statement
I've been given the line element given below in the relevant equations section and I need to prove that the space it represents is just the same as the 2-D Euclidean plane.
Homework Equations
[itex] ds^2 = a^2 \frac{d\eta ^2 }{cosh^4(\eta)} + a^2 tanh^2(\eta) d\theta ^2 [/itex]
Where
[itex] 0\lt\theta\leq2\pi [/itex]
[itex] 0\lt\eta\leq\infty [/itex]
The Attempt at a Solution
I'm pretty sure that to prove this I need to find the coordinate transform to show that the above line element should be equal to:
[itex] ds^2 = dx^2 + dy^2[/itex]
So I believe I'm looking for [itex]x[/itex] and [itex]y[/itex] in terms of [itex]eta[/itex] and [itex]theta[/itex], but I'm not entirely sure how to go about that.
Any suggestions are much appreciated!