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| | In [[mathematics]], a (compact) '''taut submanifold''' ''N'' of a [[space form]] ''M'' is a [[compact space|compact]] [[submanifold]] with the property that for every <math>q\in M\,</math> the [[distance function]] |
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| | :<math>L_q:N\to\mathbf R,\qquad L_q(x) = \operatorname{dist}(x,q)^2\,</math> |
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| | is a perfect [[Morse function]].{{citation needed|date=December 2012}} |
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| | If ''N'' is not compact, one needs to consider the restriction of the <math>L_q</math> to any of their [[sublevel set]]s. |
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| | ==External links== |
| | *{{springer|title=Tight and taut immersions|T/t092810|first=N.H.|last= Kuiper}} |
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| | [[Category:Differential geometry]] |
| | [[Category:Morse theory]] |
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| | {{differential-geometry-stub}} |
| | {{topology-stub}} |
Revision as of 05:19, 14 January 2014
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.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
If N is not compact, one needs to consider the restriction of the 
to any of their sublevel sets.
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Template:Differential-geometry-stub
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