Hello,
Suppose that R^2 is provided with the following metric
ds^2 = dx^2 + (\cosh(x))^2 dy^2
Can we find a general exact formula \alpha(t) for the geodesics (starting at an arbitrary point) ?
The geodesic equation gives
x'' - \cosh(x)\sinh(x) (y')^2 = 0
y'' + 2...