Fundamental Theorem of Riemannian Geometry

Theorem

Let $\struct {M, g}$ be a Riemannian or pseudo-Riemannian manifold with or without boundary.

Let $\nabla$ be a Levi-Civita connection.

Then $\nabla$ is unique.

Proof

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Source of Name

This entry was named for Bernhard Riemann.

Sources

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