2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66462Let $S^{n}$ be the $n$-sphere of constant positive curvature. For $n \geq 2$, we will show that a measure on the unit tangent bundle of $S^{2n}$, which is even and invariant under the geodesic flow, is not uniquely determined by its projection to $S^{2n}$.4 pages, To appear in Proc. Amer. Math. SocDifferential GeometryDynamical Systems53D25text