The fundamental theorem of Riemannian geometry states that a Riemannian manifold has a unique connection on its tangent bundle which has zero torsion tensor and is compatible with the Riemannian metric. This connection is called the Levi-Civita connection.
Fundamental Theorem of Riemannian Geometry
See also
Covariant Derivative, Levi-Civita Connection, Riemannian Manifold, Riemannian MetricThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Fundamental Theorem of Riemannian Geometry." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FundamentalTheoremofRiemannianGeometry.html