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Levi-Civita connection
In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold that preserves the (pseudo-)Riemannian metric and is torsion-free.
The fundamental theorem of Riemannian geometry states that there is a unique connection that satisfies these properties.
In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. The components (structure coefficients) of this connection with respect to a system of local coordinates are called Christoffel symbols.
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