計量テンソル
( x 1 , x 2 , x 3 ) = ( r , θ , φ ) {\displaystyle (x^{1},x^{2},x^{3})=(r,\theta ,\phi )\ }
g = [ 1 0 0 0 ( x 1 ) 2 0 0 0 ( x 1 sin  x 2 ) 2 ] , d s 2 = ( d r ) 2 + r 2 ( d θ ) 2 + r 2 sin 2  θ ( d φ ) 2 {\displaystyle g={\begin{bmatrix}1&0&0\\0&(x^{1})^{2}&0\\0&0&(x^{1}\sin x^{2})^{2}\end{bmatrix}},\quad ds_{}^{2}=(dr)^{2}+r^{2}(d\theta )^{2}+r^{2}\sin ^{2}\theta (d\phi )^{2}}
( x 1 , x 2 ) = ( r , θ ) {\displaystyle (x^{1},x^{2})=(r,\theta )\ }
g = [ 1 0 0 ( x 1 ) 2 ] , d s 2 = ( d r ) 2 + r 2 ( d θ ) 2 {\displaystyle g={\begin{bmatrix}1&0\\0&(x^{1})^{2}\end{bmatrix}},\quad ds_{}^{2}=(dr)^{2}+r^{2}(d\theta )^{2}}