The search for tractable models led to the study of the free motion of a particle (the geodesic flow) on surfaces of constant negative curvature.
Let us insist that special loci, which are the fixed-point sets of the action of the modular group are simultaneously algebraic, arithmetic and totally geodesic.
Since expansive geodesic flows of compact surfaces have no conjugate points, the accessibility property holds for every two-dimensional expansive geodesic flow.
We show that the metric of non-positively curved graph manifolds is determined by its geodesic flow.
Quasiconformality in the geodesic flow of negatively curved manifolds.
It follows from this that the times at which the geodesic crosses itself are isolated.
Neither do geometric geodesics prescribe our perceptual solutions in more than a few specialized cases.
A curve that satisfies (17) will be called a magnetic geodesic.
