Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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:Ntomathbf R,qquad L_q(x) = operatorname{dist}(x,q)^2, for qin M, which is a Morse function, is perfect. If N is not compact, one needs to consider the restriction of the Lq to any of their sublevel sets.
Taut Submanifold
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