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

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