Taut submanifold
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Revision as of 06:29, 7 February 2021 by imported>LinuxGuru (fix)
In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that for every [math]\displaystyle{ q\in M }[/math] the distance function
- [math]\displaystyle{ L_q:N\to\mathbf R,\qquad L_q(x) = \operatorname{dist}(x,q)^2 }[/math]
is a perfect Morse function.[citation needed]
If N is not compact, one needs to consider the restriction of the [math]\displaystyle{ L_q }[/math] 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
![]() | Original source: https://en.wikipedia.org/wiki/Taut submanifold.
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