Riemannian Metric gives rise to Connection

Theorem

Let $M$ be a smooth manifold.

Let $g$ be a Riemannian metric on $M$.

Then $g$ gives rise to a connection.

It is not necessarily the case that a connection gives rise to a Riemannian metric.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): connection
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): connection