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

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

is a perfect Morse function.

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

References

• Hazewinkel, Michiel, ed. (2001), "Tight and taut immersions", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page