\newcommand{\bea}{\begin{eqnarray}} \newcommand{\eea}{\end{eqnarray}} \bea\nn &&\Gamma_{a,\mu b}=-\frac{1}{2}(\p_a g_{b \mu}-\p_b g_{a \mu})...

\newcommand{\bea}{\begin{eqnarray}} \newcommand{\eea}{\end{eqnarray}} \bea\nn &&\Gamma_{a,\mu b}=-\frac{1}{2}(\p_a g_{b \mu}-\p_b g_{a \mu}),\h \Gamma_{a,\mu \nu}=-\frac{1}{2}\p_a g_{\mu\nu}, \\ \nn &&H_{a \mu\nu}=\p_a b_{\mu\nu},\h H_{a \mu b}=-\p_a b_{b \mu}+\p_b b_{a \mu}.\eea

\bea\label{V1} G_{00}+G_{11}=(\alpha^2+\beta^2)g_{MN}\frac{d\tilde{X}^M}{d\xi}\frac{d\tilde{X}^N}{d\xi} +2\beta\Lambda^\mu g_{\mu N} \frac{d\tilde{X}^N}{d\xi} +\Lambda^\mu\Lambda^\nu g_{\mu \nu} =0,\eea \bea\label{V2} G_{01}&=&\alpha\beta g_{MN}\frac{d\tilde{X}^M}{d\xi}\frac{d\tilde{X}^N}{d\xi}+\alpha\Lambda^\mu g_{\mu ...

\bea\nn &&-(\alpha^2-\beta^2)\left[g_{LK}\frac{d^2\tilde{X}^K}{d\xi^2}+ \Gamma_{L,MN}\frac{d\tilde{X}^M}{d\xi}\frac{d\tilde{X}^N}{d\xi}\right] +2\beta\Lambda^\mu\Gamma_{L,\mu N}\frac{d\tilde{X}^N}{d\xi} +\Lambda^\mu\Lambda^\nu \Gamma_{L,\mu\nu} \\ \label{EM} &&= \alpha\Lambda^\mu H_{L\mu N}\frac{d\tilde{X}^N}{d\xi},\eea \bea\label{Q} ...