Definition:Acceleration of Smooth Curve on Smooth Manifold
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Definition
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 $D_t$ be the covariant derivative along $\gamma$.
Then $D_t \gamma'$ is called the acceleration of $\gamma$ on $M$.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 4$: Connections. Covariant Derivatives Along Curves