Liouville surface
From HandWiki
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
- [math]\displaystyle{ z=f(x,y) }[/math]
such that the first fundamental form is of the form
- [math]\displaystyle{ ds^2 = \big(f_1(x) + f_2(y)\big)\left(dx^2+dy^2\right).\, }[/math]
Sometimes a metric of this form is called a Liouville metric. Every surface of revolution is a Liouville surface.
References
- Gelfand, I.M.; 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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