Taut submanifold

In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that every distance function

$L_q:N\to\mathbf R, L_q(x)=dist(x,q)^2$

for

$q\in M$

If N is not compact, one needs to consider the restriction of the $L q$ to any of their sublevel sets.