Let $\struct {M, g}$ be a Riemannian manifold.
Let $I = \closedint a b$ is a closed real interval.
Let $J$ is an open real interval.
Let $\Gamma : J \times I \to M$ be an admissible family of curves.
Let $\tuple {a_0, a_1, a_2, \ldots, a_{n - 1}, a_n}$ be a finite subdivision of $I$.
Then:
where $D_t$ denotes the covariant derivative along the main curve, and $D_s$ denotes the covariant derivative along the transverse curve.
![]() | This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |