- #1

Phinrich

- 82

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- TL;DR Summary
- 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