Christoffel symbols with maple

[David Hilbert]

Hi,

consider the Lobachevski plane. I would like to compute the Christoffel
symbols. I use the tensor package:

with(tensor):
coords:=[x, y]:
g:=array (symmetric, sparse, 1..2, 1..2):
g[1,1]:=(1/y2): g[2,2]:=1/y2:
metric:=create([-1,-1], eval(g));

and with

display_allGR (coords,metric,contra_metric, det_met, C1, C2, Rm, Rc, R,
G, C);

it gives

The Christoffel Symbols of the Second Kind
non-zero components :

{1,12} = - 1 / y

{2,11} = 1 / y

{2,22} = - 1 / y

I don't know if this computation is right. Everybody knows that the
straight line x=0, y=t, t > 0 is a geodesic line but one of the two
geodesics equations become

d^2(y)/dt^2 + {2,22} dy/dt dy/dt = 0

i.e.

-1/y = 0.

Why this equation isn't verified?

Thanks, DH

[saeede.h...@gmail.com]

I also want to do the same but with a difference that I don't know anything and where to start from... can anyone help me