International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 4, Pages 421-431
-tightness and curvature of submanifolds
Fachbereich Mathematik, Technische Universität Berlin, Straβe des 17. Juni 135, Berlin 12 (West) 1000, Germany
Received 2 August 1978
Copyright © 1978 Wolfgang Kühnel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The purpose of this note is to establish a connection between the notion of -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 -tightness.