Taut submanifold

In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that for every <math>q\in M</math> the distance function

<math>L_q:N\to\mathbf R,\qquad L_q(x) = \operatorname{dist}(x,q)^2</math>

is a perfect Morse function.Template:Citation needed

If N is not compact, one needs to consider the restriction of the <math>L_q</math> to any of their sublevel sets.

References

• Template:Springer