In mathematics—specifically, in Riemannian geometry—a Wiedersehen pair is a pair of distinct points x and y on a (usually, but not necessarily, two-dimensional) compact Riemannian manifold (M, g) such that every geodesic through x also passes through y, and the same with x and y interchanged.
For example, on an ordinary sphere where the geodesics are great circles, the Wiedersehen pairs are exactly the pairs of antipodal points.
The concept was introduced by the Austro-Hungarian mathematician Wilhelm Blaschke and comes from the German term meaning "seeing again".
As it turns out, in each dimension n the only Wiedersehen manifold (up to isometry) is the standard Euclidean n-sphere.
Initially known as the Blaschke conjecture, this result was established by combined works of Berger, Kazdan, Weinstein (for even n), and Yang (odd n).