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 Can we express thew Christoffel Symbols in terms of the change of basis?
Hi All
Given that the Riemann Curvature Tensor may be derived from the parallel Transport of a Vector around a closed loop, and if that vector is a covariant vector
Having contravariant basis
The calculation gives the result
Now:
Given that the Christoffel Symbols represent the change in the basis vectors (rotations etc) as we move around the closed loop and given that mathematically this is given by
Can we represent the Riemann Curvature Tensor in terms of the basis
Thank You
Given that the Riemann Curvature Tensor may be derived from the parallel Transport of a Vector around a closed loop, and if that vector is a covariant vector
Having contravariant basis
The calculation gives the result
Now:
Given that the Christoffel Symbols represent the change in the basis vectors (rotations etc) as we move around the closed loop and given that mathematically this is given by
Can we represent the Riemann Curvature Tensor in terms of the basis
Thank You
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