Tight analytic immersions of highly connected manifolds

Abstract

An immersion of a manifold which minimizes total absolute curvature is called tight. In this paper we determine which ( k − 1 ) (k - 1) -connected (but not k k -connected) manifolds of dimension 2 k 2k , with trivial k k th Stiefel-Whitney class, admit codimension 2 2 tight analytic immersions.