View source for Liouville surface

{{TEX|done}}{{MSC|53A05}}

A surface for which the equations of the geodesics admit a quadratic integral $a_{ij} du^i du^j$, where the tensor $a_{ij}$ is distinct from the [[metric tensor]] $g_{ij}$ of the surface. For example, a surface of constant [[Gaussian curvature]] is a Liouville surface. For a surface to admit a [[geodesic mapping]] onto a plane it is necessary and sufficient that it be a Liouville surface (Dini's theorem). See also [[Liouville net]].

====References====
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<TR><TD valign="top">[a1]</TD> <TD valign="top"> W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie", Springer  (1973)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Berger, B. Gostiaux, "Differential geometry: manifolds, curves, and surfaces", Springer  (1988)  (Translated from French)</TD></TR>
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