International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1978 / Article

Open Access

Volume 1 |Article ID 191250 | 11 pages | https://doi.org/10.1155/S0161171278000423

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

Received02 Aug 1978

Abstract

The purpose of this note is to establish a connection between the notion of (n2)-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 (n2)-tightness.

Copyright © 1978 Hindawi Publishing Corporation. 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.

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