In the mathematical field of differential geometry a Liouville surface (named after Joseph Liouville) is a type of surface which in local coordinates may be written as a graph in R3 z = f ( x , y ) {\displaystyle z=f(x,y)} such that the first fundamental form is of the form d s 2 = ( f 1 ( x ) + f 2 ( y ) ) ( d x 2 + d y 2 ) . {\displaystyle ds^{2}={\big (}f_{1}(x)+f_{2}(y){\big )}\left(dx^{2}+dy^{2}\right).} Sometimes a metric of this form is called a Liouville metric.
In the mathematical field of differential geometry a Liouville surface (named after Joseph Liouville) is a type of surface which in local coordinates may be written as a graph in R3 z = f ( x , y ) {\displaystyle z=f(x,y)} such that the first fundamental form is of the form d s 2 = ( f 1 ( x ) + f 2 ( y ) ) ( d x 2 + d y 2 ) . {\displaystyle ds^{2}={\big (}f_{1}(x)+f_{2}(y){\big )}\left(dx^{2}+dy^{2}\right).} Sometimes a metric of this form is called a Liouville metric.
Source: Wikipedia "Liouville surface" · CC BY-SA 4.0
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