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Display information for equation id:math.1107.465 on revision:1107
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\begin{align}
& \frac{d{{s}^{2}}{{|}_{{{{\bar{x}}}^{0}}+\delta {{{\bar{x}}}^{0}}=\text{const}}}}{d{{s}^{2}}{{|}_{{{{\bar{x}}}^{0}}=\text{const}}}}=1+\delta {{{\bar{x}}}^{0}}h\left( {{{\bar{x}}}^{0}} \right)+O\left( {{\left( \delta {{{\bar{x}}}^{0}} \right)}^{2}} \right) \\
& \Rightarrow {{g}_{ik}}\left( {{{\bar{x}}}^{0}},{{x}^{k}} \right)={{S}^{2}}\left( {{{\bar{x}}}^{0}} \right){{\gamma }_{ij}}\left( {{x}^{k}} \right) \\
& \Rightarrow d{{s}^{2}}={{\left( d{{{\bar{x}}}^{0}} \right)}^{2}}+{{S}^{2}}\left( {{{\bar{x}}}^{0}} \right){{\gamma }_{ij}}\left( {{x}^{k}} \right) \\
\end{align}
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