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Differential geometry

  1. Sep 7, 2008 #1
    Hello all,

    I am taking a class on differential geometry and I have run into a problem with the following question:

    Show that if α is a regular curve, i.e., ||α'(t)|| > 0 for all t ∈ I, then s(t) is an invertible function, i.e., it is one-to-one (Hint: compute s'(t) ).

    I am not really sure what the hint is getting at and don't really know how I should be aproaching this problem.
    Any help would be greatly appreciated : )

    thanks in advanced!
  2. jcsd
  3. Sep 7, 2008 #2


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    Perhaps it would be a good idea to say what relation the curve α has to s(t)! Are we to assume that s(t) is the arclength of a portion of α?
  4. Sep 8, 2008 #3
    Right, my appologies. s(t) is the arclength of the curve relative to some point say t=a.
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