The total absolute curvature and the total absolute torsion of open curves in the Euclidean spaces

2016 ◽  
pp. 41-48
Author(s):  
Kazuyuki Enomoto ◽  
Jin-ichi Itoh
Keyword(s):  
Euclidean Spaces ◽  
Total Absolute Curvature ◽  
Absolute Curvature

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

1978 ◽  
Vol 1 (4) ◽  
pp. 421-431 ◽  
Author(s):  
Wolfgang Kühnel
Keyword(s):  
Euclidean Space ◽  
Geometric Inequality ◽  
Total Absolute Curvature ◽  
Absolute Curvature

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.

scholarly journals The total absolute curvature of open curves in $E^{3}$

2008 ◽  
Vol 52 (1) ◽  
pp. 47-76 ◽  
Author(s):  
Kazuyuki Enomoto ◽  
Jin-ichi Itoh ◽  
Robert Sinclair
Keyword(s):  
Total Absolute Curvature ◽  
Absolute Curvature
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