Taut submanifold

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

L_{q}:N\to \mathbf {R} ,\qquad L_{q}(x)=\operatorname {dist} (x,q)^{2}

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

References

Kuiper, N.H. (2001) [1994], "Tight and taut immersions", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4

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