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The Christoffel symbols are the array of numbers describing a metric connection in a non-flat surface.

I am unclear and having trouble picturing Christoffel symbols in 4 dimensions used in general relativity, could anyone give some pointers to the simplest/lowest dimension for which Christoffel symbols are defined, please?

1. What is the lowest dimension for which Christoffel symbols exist?

2. Are there Christoffel symbols in 1 dimension, or if not, in 2 dimensions?

3. What does the form of Christoffel symbol look like in 1 dimension (or lowest dimension), and which rate of change in the coordinate bases is it computing?

Thank you for any help/pointers on this.

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Answer to all three questions: in dimension $1$, the Levi-Civita connection has $\Gamma_{00}^0=\frac12g^{00}\partial_0g_{00}$.

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