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Exercise [12.05]
http://www.roadtoreality.info/viewtopic.php?f=19&t=203
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Author:  Sameed Zahoor [ 30 Aug 2008, 11:13 ]
Post subject:  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.

Author:  DimBulb [ 22 Jul 2009, 18:16 ]
Post subject:  Re: Exercise [12.05]

What about the "represents the tangent hyperplane elements to x^2 = constant" part of the exercise? How is that shown?

Author:  jbeckmann [ 16 Sep 2010, 15:37 ]
Post subject:  Re: Exercise [12.05]

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