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 R^{3}

z = f(x,y)

such that the first fundamental form is of the form

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

**References**

* Gelfand, I.M. and Fomin, S.V. (2000). Calculus of variations. Dover. ISBN 0-486-41448-5. (Translated from the Russian by R. Silverman.)

* Guggenheimer, Heinrich (1977). "Chapter 11: Inner geometry of surfaces", Differential Geometry. Dover. ISBN 0-486-63433-7.

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