A Property of Geodesics in Special K\"ahler Geometry

We study the stable geodesics of the QFT special K\"ahler geometry ($\equiv$ Seiberg-Witten geometry of 4d $\mathcal{N}=2$ QFT) using the Myers argument. Complete stable geodesics are quite restricted, and can be described very explicitly. In particular no closed stable geodesic exists. We comment on the application of the Myers method to related problems, including geodesics in moduli spaces of Calabi-Yau 3-folds.