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 Exercise [12.05] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [12.05]
Let,
\alpha=\alpha_1 dx^1 +\alpha_2 dx^2+...+\alpha_{n} dx^{n}
be a general covector field.
Then the covector dx^2 is a covector field with a certain set of components \alpha_{i}.The components can be determined by equating dx^{2} to \alpha.
Hence,
dx^2=\alpha_1 dx^1 +\alpha_2 dx^2+...+\alpha_{n} dx^{n}
As long as dx^{i} and dx^{j} are linearly independent for i not equal to j,the components (\alpha_1,\alpha_2,...,\alpha_{n})can be seen to be (0,1,0,...,0) by simply equating the coefficients ofdx^{i} on both sides.


30 Aug 2008, 11:13

Joined: 07 May 2009, 16:45
Posts: 62
Post Re: Exercise [12.05]
What about the "represents the tangent hyperplane elements to x^2 = constant" part of the exercise? How is that shown?


22 Jul 2009, 18:16

Joined: 22 Apr 2010, 15:52
Posts: 43
Location: Olpe, Germany
Post Re: Exercise [12.05]
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16 Sep 2010, 15:37
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