Total Absolute Curvature:

Given a mapping f of a surface M into space, the total absolute curvature is
where K is the Gaussian curvature. It can be shown [More] that the total absolute curvature is always at least 4 - X(M) where X(M) represents the Euler characteristic of M. When equality holds, the mapping is called tight.


[TOC] [Index] [Glossary] [Mail] [Help]


8/12/94 dpvc@geom.umn.edu -- The Geometry Center