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 

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Differential geometry Morse theory Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Office of Emergency Management Scaliger (crater) Look at other dictionaries: List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia List of differential geometry topics — This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. Contents 1 Differential geometry of curves and surfaces 1.1 Differential geometry of curves 1.2 Differential… …   Wikipedia Foliation — In mathematics, a foliation is a geometric device used to study manifolds. Informally speaking, a foliation is a kind of clothing worn on a manifold, cut from a striped fabric. On each sufficiently small piece of the manifold, these stripes give… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”