1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normal one-forms

  1. Jun 3, 2008 #1
    I'm reading through Schutz's first course in relativity book and am finding question 12 on page 83 a bit problematic.

    If I understand it correctly an normal one-form to a plane is a one-form that, when operating on a normal vector to the plane, will give the result 0. This seems fairly straight forward to me.
    The question is talking about the plane x=0.
    So all vectors normal to this must be of the form (a,0,0) (ie parallel to the x axis)
    In that case, the normal one form must have components (0,b,c) then
    [tex]\tilde{n}(\vec{V})= 0*a+b*0+c*0=0[/tex]

    Part (c) of the question says
    and the answer provided is:
    But my understanding is that (0,0,[tex]\beta[/tex]) is just a subset of all possible normal one forms to this plane, and I'd agree that of this subset any [tex]\tilde{n}[/tex] is a multiple of any other. But this isn't true for all [tex]\tilde{n}[/tex], as surley (0,[tex]\alpha, \beta[/tex]) is also valid.

    Obviously I'm missing something fairly fundamental here, and I just have to understand this before I move on... Please help :)
  2. jcsd
  3. Jun 3, 2008 #2
    Oh... I am being stupid.. Just realised that the one-form has to operate on a vector tangent to the surface, not the vector normal... I really should read more carefully....:blushing:
    now the one-form is actually perpendicular to the plane and so calling it a normal one-form to the plane makes much more sense!
    Last edited: Jun 3, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Normal one-forms
  1. Normal form for Cubic (Replies: 1)

  2. Confused about one forms (Replies: 15)