Mapping preserving distance

  • Thread starter whattttt
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  • #1
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Main Question or Discussion Point

Can someone please exPlain to me what the phrase. Which metric do we have to impose in order that the mapping preserves distance means.
The example I have is
((-),phi)--->(x,y) =
(2a tan(theta/2)cos(phi) ,
2a tan(theta/2)sin(phi)) thanks
 

Answers and Replies

  • #2
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It means you need to find a metric [tex]\delta[/tex] such that for all [tex](\theta,\phi)[/tex] you have [tex]\delta(\theta,\phi)=\delta(2a\tan(\theta/2)\cos\phi,2a\tan(\theta/2)\sin\phi)[/tex].
 
  • #3
18
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I guess it will be a diagonal metric but could you possibly give me a hint how to work out the other2 entries. Thanks
 

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