On the total absolute curvature of closed curves in spheres

1986 ◽  
Vol 57 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Eberhard Teufel
Keyword(s):  
Closed Curves ◽  
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.

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