
Journal for Geometry and Graphics 19 (2015), No. 2, 179188 Copyright Heldermann Verlag 2015 A Property of Liouville Surfaces and Manifolds CalinSerban Barbat Dieselstr. 19, 80993 München, Germany calin.barbat@web.de We use the definition of the energy of a curve on a surface and show that in a Liouville surface the energy integrals along the diagonals of a net rectangle (Liouville maps are conformal) are equal. This result allows a generalization to Liouville manifolds, which is stated and proved in this paper. A series of different surfaces with an induced Liouville metric are given in Euclidean spaces. One example is given in the pseudoEuclidean (Minkowski) plane. The material presented here also relates to our previous article in this journal [Journal of Geometry and Graphics 18 (2014) 721]. Keywords: Energy/action of curve, Liouville metric, Liouville surface, Liouville manifold. MSC: 53A05; 53A07 [ Fulltextpdf (241 KB)] 