Bateman–Horn conjecture: Difference between revisions

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→‎Definition: I changed "P(x) is the fraction of" to "P(x) is the number of" cf. the paper of Bateman and Horn, "A heuristic asymptotic formula concerning the distribution of prime numbers"
 
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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>
 
is a perfect [[Morse function]].{{citation needed|date=December 2012}}
 
If ''N'' is not compact, one needs to consider the restriction of the <math>L_q</math> to any of their [[sublevel set]]s.
 
==External links==
*{{springer|title=Tight and taut immersions|T/t092810|first=N.H.|last= Kuiper}}
 
[[Category:Differential geometry]]
[[Category:Morse theory]]
 
{{differential-geometry-stub}}
{{topology-stub}}

Latest revision as of 15:32, 6 October 2014

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