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
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.
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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.
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