∂$_{ξ}$ i ( | ξ | . z k ( x, ξ | ξ | , t )) = 1 | ξ | 2 n ∑ j =2 g$_{ij}$ ξ j ( | ξ | . z k ( x, ξ | ξ | , t )) + | ξ $_{|}$  − n ∑ s =1 ( ∂$_{ν}$ s . z k ) 1 | ξ | $_{3}$ξ s n ∑ j =2 g$_{ij}$ ξ j + 1 | ξ | ∂$_{ν}$ i . z k   , (A.5) ∂ 2 ξ 1 ( | ξ | . z k ( x, ξ | ξ | , t )) = 1 | ξ | . z k − ( ξ $^{1}$) 2 | ξ | 3 . z k − n ∑ j =2 ξ j | ξ | $_{2}$∂$_{ν}$ j . z k − 2 ξ 1 | ξ | $_{2}$∂$_{ν}$ 1 . z k +2 ξ 1 n ∑ j =1 ξ $^{j}$ξ 1 | ξ | 4 ∂$_{ν}$ j . z k + ξ 1 | ξ | 2   n ∑ j =1 − ξ $^{j}$ξ 1 | ξ | 2 ∂$_{ν}$ j . z k + ∂$_{ν}$ 1 z k   n + j =1 ξ $^{j}$ξ 1 | ξ | 3 ( n ∑ i =1 ξ $^{i}$ξ 1 | ξ | 2 ∂$_{ν}$ i ∂$_{ν}$ j . z k − ∂$_{ν}$ j ∂$_{ν}$ 1 . z k ) − n ∑ j =1 ξ $^{j}$ξ 1 | ξ | 3 ∂$_{ν}$ 1 ∂$_{ν}$ j . z k + 1 | ξ | ∂ 2 ν 1 . z $^{k}$, (A.6) ∂$_{ξ}$ i ∂$_{ξ}$ 1 ( | ξ | . z k ( x, ξ | ξ | , t )) = − ξ 1 | ξ | $_{3}$( n ∑ j =2 g$_{ij}$ ξ $^{j}$) . z k −   n ∑ j =1 . z k ν j ξ $^{j}$ξ 1 | ξ | 4     n ∑ j =2 g$_{ij}$ ξ j   + . z k ν i ξ 1 | ξ | 2 + 2   n ∑ j =1 . z k ν j ξ $^{j}$ξ 1     1 | ξ | 4 n ∑ j =2 g$_{ij}$ ξ j   − . z k ν i ξ 1 | ξ | 2 + n ∑ j =1 ξ $^{j}$ξ 1 | ξ | 3 ( n ∑ m =1 . z k ν $^{j}$νm 1 | ξ | $_{2}$ξ m n ∑ s =2 g$_{is}$ξ s − . z k ν $^{i}$νj ) − n ∑ j =1 . z k ν $^{j}$ν 1 1 | ξ | $_{3}$ξ j n ∑ j =2 g$_{ij}$ ξ j + 1 | ξ | . z k ν $^{i}$ν 1 , (A.7) 20