Re: Again on Lobachevskij

[David Hilbert]
Hi,

the equations of the geodesics computed by maple for
the Lobachevskij plane (semi-plane (u,v) with v > 0) are


diff(u(t), t, t)-2*diff(u(t), t)*diff(v(t), t)/v = 0,

diff(v(t), t, t)+diff(u(t), t)2/v-diff(v(t), t)2/v = 0.

They're even available in the help for "geodesics".
I don't understand why the geodesic line
u = 0, v = t, t > 0 does not verify the system.

Thanks, DH

G. A. Edgar wrote:
u=0 satisfies the first .
v=t is not geodesic .

However,

u(t) = 0
v(t) = A*exp(b*t)

satisfies both equations, and is the same curve
as the previous one, just parametrized differently.

Jim Burns
.

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