(n-2)-tightness and curvature of submanifolds with boundary

Abstract

The purpose of this note is to establish a connection between the notion of (n−2)-tightness in the sense of N.H. Kuiper and T.F. Banchoff and the total absolute curvature of compact submanifolds-with-boundary of even dimension in Euclidean space. The argument used is a certain geometric inequality similar to that of S.S. Chern and R.K. Lashof where equality characterizes (n−2)-tightness.