Wiedersehen pair
In mathematics—specifically, in Riemannian geometry—a Wiedersehen pair is a pair of distinct points x and y on a compact Riemannian manifold such that every geodesic through x also passes through y.
For example, on an ordinary sphere where the geodesics are great circles, the Wiedersehen pairs are exactly the pairs of antipodal points.
If every point of an oriented manifold belongs to a Wiedersehen pair, then is said to be a Wiedersehen manifold. 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 is the standard Euclidean n-sphere. Initially known as the Blaschke conjecture, this result was established by combined works of Berger, Kazdan, Weinstein, and Yang.
