Definition 3.1 (Normal coordinates) . [04ZE] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Definition 3.1 (Normal coordinates).
For any ( q , v ) ∈ 𝔖 0 (q,v)\in\mathfrak{S}_{0} v = ∑ α = 1 k 0 v α e α v=\sum\limits_{\alpha=1}^{k_{0}}v_{\alpha}e_{\alpha}
(3.5) { x j ( Exp P ( q , v ) ) ≡ x j ′ ( q ) , 1 ≤ j ≤ m − k 0 , y β ( Exp P ( q , v ) ) ≡ v β , 1 ≤ β ≤ k 0 . \displaystyle\begin{cases}x_{j}(\Exp_{P}(q,v))\equiv x_{j}^{\prime}(q),&1\leq j\leq m-k_{0},\\
y_{\beta}(\Exp_{P}(q,v))\equiv v_{\beta},&1\leq\beta\leq k_{0}.\end{cases}