Non-integrability of geodesic flow on certain algebraic surfaces
  This paper addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface $x y z=1$. We prove this is the case using the Morales-Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result. 
Thomas Waters
math.DS math.DG nlin.CD