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Differential geometry 
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#1
Dec1408, 03:43 PM

P: 11

Given [tex]\{(u,v)\inR^2:u^2+v^2<1\}[/tex] with metric [tex]E = G =\frac{4}{(1u^2v^2)^2}[/tex] and [tex]F = 0[/tex]. How can I show that a Euclidean circle centered at the origin is a hyperbolic circle?



#2
Dec1508, 04:32 AM

P: 255

Note: rotations about the origin preserve this metric.



#3
Dec1608, 11:28 PM

P: 11

Given [tex]\{(u,v)\inR^2:u^2+v^2<1\}[/tex] with metric [tex]E = G =\frac{4}{(1u^2v^2)^2}[/tex] and [tex]F = 0[/tex].
With a Euclidean circle centered at the origin with radius r, how can I find the hyperbolic radius by integrating [tex]\sqrt(E(u')^2+2Fu'v'+G(v')^2)[/tex], what parametrized curve should I use? 


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