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This category contains definitions related to Geodesics.
Related results can be found in Category: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 $\nabla$.


$\forall t \in I : D_t \gamma' = 0$.

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

Pages in category "Definitions/Geodesics"

The following 4 pages are in this category, out of 4 total.