
#1
Jun308, 05:48 AM

P: 63

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 oneform to a plane is a oneform 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 Obviously I'm missing something fairly fundamental here, and I just have to understand this before I move on... Please help :) 



#2
Jun308, 05:58 AM

P: 63

Oh... I am being stupid.. Just realised that the oneform has to operate on a vector tangent to the surface, not the vector normal... I really should read more carefully....
now the oneform is actually perpendicular to the plane and so calling it a normal oneform to the plane makes much more sense! 


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