Liouville surface

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


 * $$z=f(x,y)$$

such that the first fundamental form is of the form


 * $$ds^2 = \big(f_1(x) + f_2(y)\big)\left(dx^2+dy^2\right).\,$$

Sometimes a metric of this form is called a Liouville metric. Every surface of revolution is a Liouville surface.