The unchanged original rods

Displayed formulas in this passage

• XX-C@1#eq:Crod · line 557

  $$(\mathcal{C}z{)}^{ia}=\frac{1}{2a^2}{\delta }^{ia}{\delta }^{jk}{h}_{jk}-a^{-2}{h}_{ia}-\frac{p}{A}{\delta }^{ia}\phi .$$

• XX-C@1#eq:rodinverse · line 566

  $$\begin{array}{rlrl}({\mathsf{G}}_{\mathrm{sp}}b)(\mathbf{x})& =-\frac{1}{4\pi }{\int }_{{\mathbb{R}}^3}\frac{b(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}{\mathrm{d}}^{3}y,& \Delta {\mathsf{G}}_{\mathrm{sp}}b& =b,\\ (\mathcal{R}z{)}^a={Y_1}^a& =-{\mathsf{G}}_{\mathrm{sp}}{\partial }_i(\mathcal{C}z{)}^{ia}.& & \end{array}$$

• XX-C@1#eq:dipole · line 578

  $$(\mathcal{R}z{)}^a(\mathbf{x})=-\frac{1}{4\pi }{\int }_{{\mathbb{R}}^3}\frac{x_i-y_i}{|\mathbf{x}-\mathbf{y}{|}^3}(\mathcal{C}z{)}^{ia}(\mathbf{y}){\mathrm{d}}^{3}y.$$

• XX-C@1#eq:originalrods · line 587

  $${\partial }_i\left(\sqrt{\det {\gamma }_s}{{\gamma }_s}^{ij}{\partial }_j{R}_s^a\right)=0,{R_s}^a-x^a⟶0(|\mathbf{x}|\to \infty ).$$

• unlabeled · line 531

  $$g_s=\bar{g}+sh+\frac{s^2}{2}k,{\varphi }_s=\bar{\varphi }+s\phi +\frac{s^2}{2}\psi ,T_s=t_{\ast }{e}^{({\varphi }_s-{\varphi }_{\ast })/A}.$$

• unlabeled · line 538

  $$N_s={\left(-{g_s}^{-1}(\mathrm{d}{\varphi }_s,\mathrm{d}{\varphi }_s)\right)}^{-1/2},$$

• unlabeled · line 544

  $$u_1=-\frac{t}{A}\phi .$$

• unlabeled · line 548

  $$({\gamma }_1{)}_{ij}=h_{ij}+2a^{2}H{u}_1{\delta }_{ij}.$$

• unlabeled · line 552

  $$C=a^{-2}{\gamma }_1,B_1=\frac{1}{2}(\mathrm{tr}C)I-C,$$