So, it is defined that:(adsbygoogle = window.adsbygoogle || []).push({});

Γ^{λ}_{μ}_{υ}= Γ^{λ}_{μ}_{υ}+ δΓ^{λ}_{μ}_{υ}

This makes obvious to see that the variation of the connection, which is defined as a difference of 2 connections, is indeed a tensor.

Therefore we can express it as a sum of covariant derivatives.

δΓ^{λ}_{μ}_{υ}= ½g^{λ}^{ν}(-∇_{λ}δg_{μ}_{ν}+ ∇_{μ}δg_{λ}_{ν}+ ∇_{ν}δg_{λ}_{μ})

However, I do not know how to make this step. Help?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Variation of the Christoffel Symbols

**Physics Forums | Science Articles, Homework Help, Discussion**