ANTIPODAL SETS IN ORIENTED REAL GRASSMANN MANIFOLDS

Abstract

We reduce the problem of classifying all maximal antipodal sets in the oriented real Grassmann manifold [Formula: see text] 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 [Formula: see text] for k ≤ 4. We construct some maximal antipodal subsets for higher k.