Jacobi Vector Fields of Integrable Geodesic Flows

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic line and construct the formula for the normal part of the Jacobi field. If a geodesic line is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic line is hyperbolic) than we can construct the fundamental solution of Jacobi equation $\ddot{u} = -K(t) u$. That was done for quadratically integrable geodesic flows.