Taut submanifold

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

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

for

$q\in M\,$

which is a Morse function, is perfect.

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

External links

• Kuiper, N.H. (2001), "Tight and taut immersions", in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Springer, ISBN 978-1556080104, http://eom.springer.de/default.htm 

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