${{{ \delta} _u} _v} = {\overset{u\downarrow(\rightarrow[{i\downarrow)\rightarrow[{v\downarrow(\rightarrow[{j\downarrow)\rightarrow}]}]}]}{\left[ \begin{matrix} 1 & 0 \\ 0 & {{ \delta} _i} _j\end{matrix} \right]}}$
${{{ \eta} _u} _v} = {\overset{U\downarrow V\rightarrow}{\left[ \begin{matrix} -1 & 0 \\ 0 & {{ \delta} _i} _j\end{matrix} \right]}}$
${{{ g} _u} _v} = {{{{ \eta} _u} _v} - {{{2}} {{\Phi}} \cdot {{{{ \delta} _u} _v}}}}$
${{{ g} ^u} ^v} = {\overset{U\downarrow V\rightarrow}{\left[ \begin{matrix} \frac{-1}{{1} + {{{2}} {{\Phi}}}} & 0 \\ 0 & \frac{{{ \delta} ^i} ^j}{{1} - {{{2}} {{\Phi}}}}\end{matrix} \right]}}$
${{{{ \Gamma} _a} _b} _c} = {{\frac{1}{2}}{\left({{{{{{ g} _a} _b} _{,c}} + {{{{ g} _a} _c} _{,b}}} - {{{{ g} _b} _c} _{,a}}}\right)}}$
${{{{ g} _u} _v} _{,w}} = {{\left( {\overset{U\downarrow V\rightarrow}{\left[ \begin{matrix} -1 & 0 \\ 0 & {{ \delta} _i} _j\end{matrix} \right]}} - {{{2}} {{\Phi}} \cdot {{\overset{u\downarrow(\rightarrow[{i\downarrow)\rightarrow[{v\downarrow(\rightarrow[{j\downarrow)\rightarrow}]}]}]}{\left[ \begin{matrix} 1 & 0 \\ 0 & {{ \delta} _i} _j\end{matrix} \right]}}}}\right)} _{,w}}$
${{{{ \Gamma} ^a} _b} _c} = {{{{{ g} ^a} ^d}} {{{{{ \Gamma} _d} _b} _c}}}$