Liouville surface

In the mathematical field of differential geometry a Liouville surface 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

:$ds^2\; =\; (f\_1(x)\; +\; f\_2(y))(dx^2+dy^2).,$

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

References

* (Translated from the Russian by R. Silverman.)

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