Fundamental Theorem of Riemannian Geometry

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

See also

Covariant Derivative, Levi-Civita Connection, Riemannian Manifold, Riemannian Metric

This entry contributed by Todd Rowland

Explore with Wolfram|Alpha

Cite this as:

Rowland, Todd. "Fundamental Theorem of Riemannian Geometry." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications