= Geodesic hyperbolicity from negative Gaussian curvature
{title2=$Q(y,z)=yz,\qquad \dot Q=z^2-Ky^2$}
A perpendicular <Jacobi field> on a <Riemannian surface> has scalar equation $\ddot y+Ky=0$. For strictly negative curvature on a <closed manifold>, the displayed derivative is uniformly positive definite, so the <quadratic-form criterion for an Anosov flow> makes the <geodesic flow> Anosov. When $K=-1$, the stable and unstable lines in the canonical frame are respectively $\mathbb R(H-V)$ and $\mathbb R(H+V)$, with factors $e^{-t}$ and $e^t$.
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