Liouville surface

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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.

[edit] 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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