Classically, tightness is defined in terms of the total absolute
curvature:
\tau(f)={1\over 2\pi}\int_M K\,dA.
It is possible to show that $\tau(f)\ge 4\chi(M)$,
and when equality holds, $f$ is tight.
This definition is only valid for smooth immersions, but the
twopiece property makes sense even in the polyhedral case.
