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