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

is a perfect Morse function.[citation needed]

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

References

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  • Kuiper, N.H. (2001) [1994], "Tight and taut immersions", Encyclopedia of Mathematics, EMS Press