Measures Invariant under the Geodesic Flow and their Projections

Abstract

Let $S^n$ be the $n$-sphere of constant positive curvature. For $n\ge 2$, 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. Soc