Codimension One and Two Immersions of Grassmann Manifolds in Euclidean Spaces

Abstract

1 Introduction Let G_(m,n) be the Grassmann manifold of the unoriented, m-dimensional vector subspaces of the vector space R~(m+n). Then G_(m,n) is a closed, smooth manifold of dimension mn. G_(m,n)≌G_(n,m), and G_(1,n)≌G_(n,1) is just the real projective space RP~n. For convenience, we assume that m≤n. Suppose M~pR~q means that the p-dimensional manifold M~p is immersed in q-