Antipodal sets in oriented real Grassmann manifolds

Abstract

We reduce the problem of classifying all maximal antipodal sets in the oriented real Grassmann manifold G̃k(Rn) to that of classifying all maximal subsets satisfying certain conditions in the set consisting of subsets of cardinality k in {1, ..., n}. Using this reduction we classify all maximal antipodal sets in G̃k(Rn) for k ≤ 4. We construct some maximal antipodal subsets for higher k. © World Scientific Publishing Company.