
#1
Apr2308, 08:16 PM

P: 1

Hello,
Suppose that [tex]R^2[/tex] is provided with the following metric [tex] ds^2 = dx^2 + (\cosh(x))^2 dy^2 [/tex] Can we find a general exact formula [tex]\alpha(t)[/tex] for the geodesics (starting at an arbitrary point) ? The geodesic equation gives [tex] x''  \cosh(x)\sinh(x) (y')^2 = 0 [/tex] [tex] y'' + 2 \tanh(x) x' y' = 0 [/tex] I guess that since this model is simply a reparametrization of the Hyperbolic space on R^2 the geodesics should be known ? Thank you 


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