# Category:Geodesics

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This category contains results about **Geodesics**.

Definitions specific to this category can be found in Definitions/Geodesics.

Let $M$ be a smooth manifold with or without boundary.

Let $I \subseteq \R$ be a real interval.

Let $\gamma : I \to M$ be a smooth curve on $M$.

Let $\gamma'$ be the velocity of $\gamma$.

Let $\nabla$ be a connection on $M$.

Let $D_t$ be the covariant derivative along $\gamma$ with respect to $\nabla$.

Suppose:

- $\forall t \in I : D_t \gamma' = 0$.

Then $\gamma$ is called the **geodesic (with respect to $\nabla$)**.

## Pages in category "Geodesics"

The following 7 pages are in this category, out of 7 total.