Definition:Christoffel Symbol

Definition

Let $\struct {M, g}$ be a Riemannian or pseudo-Riemannian manifold.

Let $\nabla$ be the Levi-Civita connection of $\struct {M, g}$.

Suppose $\Gamma^k_{ij}$ are the connection coefficients of $\nabla$.

Then $\Gamma^k_{ij}$ are called the Christoffel symbols.

Also see

• Results about the Christoffel symbols can be found here.

Source of Name

This entry was named for Elwin Bruno Christoffel.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 5$: The Levi-Civita Connection. Symmetric Connections

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