# Tag Info

No, in general, they don't close. (Though, as you say, some geodesics do.) Consider, for example, an oblate ellipsoid of revolution, and take two points on its equator such that the angle $\alpha$ between them is not a rational multiple of $\pi$. On a sphere, the only geodesic passing through tho points on the equator is the equator; but in our case, since ...