Geodesic
A Property of Liouville Surfaces and Manifolds
Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 179-188 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 pseudo-Euclidean (Minkowski) plane. The material presented here also relates to our previous article in this journal [Journal of Geometry and Graphics 18 (2014) 7--21].
Classification : 53A05, 53A07
Mots-clés : Energy/action of curve, Liouville metric, Liouville surface, Liouville manifold 
@article{JGG_2015_19_2_JGG_2015_19_2_a1,
     author = {C.-S. Barbat },
     title = {A {Property} of {Liouville} {Surfaces} and {Manifolds}},
     journal = {Journal for geometry and graphics},
     pages = {179--188},
     year = {2015},
     volume = {19},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a1/}
}
TY  - JOUR
AU  - C.-S. Barbat 
TI  - A Property of Liouville Surfaces and Manifolds
JO  - Journal for geometry and graphics
PY  - 2015
SP  - 179
EP  - 188
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a1/
ID  - JGG_2015_19_2_JGG_2015_19_2_a1
ER  - 
%0 Journal Article
%A C.-S. Barbat 
%T A Property of Liouville Surfaces and Manifolds
%J Journal for geometry and graphics
%D 2015
%P 179-188
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a1/
%F JGG_2015_19_2_JGG_2015_19_2_a1
C.-S. Barbat . A Property of Liouville Surfaces and Manifolds. Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 179-188. http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a1/