  An immersion of a compact manifold is tight if it admits the minimal total
absolute curvature over all immersions of the manifold. A prominent result in
the study of minimal total absolute curvature immersions is the theorem of
Chern and Lashof, which characterizes minimal total absolute curvature
immersions, and tight immersions, of spheres into a Euclidean space. In this
paper we examine tight immersions of highly connected manifolds; i.e.,
2k-dimensional manifolds that are (k-1)-connected by not k-connected, and
characterize the immersions of highest codimension.
