000114945 001__ 114945
000114945 005__ 20190316234109.0
000114945 037__ $$aARTICLE
000114945 245__ $$aL'horizon de SOL
000114945 269__ $$a1998
000114945 260__ $$c1998
000114945 336__ $$aJournal Articles
000114945 520__ $$aThe goal of this paper is to give an explicit analysis of the geodesic flow on the three dimensional Lie group SOL. In particular we describe its horizon. (The horizon of a riemannian manifold is a topological space parametrizing the asymptotic classes of geodesic rays.) We begin the paper by a brief exposition of some known results about the asymptotic behaviour of the geodesics in manifolds of negative and positive curvature. Sections two and three present the necessary notions of SOL geometry and the equations of the geodesics are integrated in section 4. In Section 5, we classify the geodesics in three types according to their geometric behaviour (reflecting the non isotropic character of SOL geometry) and in Section 6 we finally compute the horizon.
000114945 700__ $$g106581$$aTroyanov, Marc$$0241796
000114945 773__ $$j16$$tExpo. Math.$$k5$$q441-479
000114945 8564_ $$zURL
000114945 8564_ $$uhttps://infoscience.epfl.ch/record/114945/files/TroyanovExposition.%20Math.1998.pdf$$zn/a$$s294154
000114945 909C0 $$xU10116$$0252207$$pGR-TR
000114945 909CO $$qGLOBAL_SET$$pSB$$ooai:infoscience.tind.io:114945$$particle
000114945 937__ $$aGR-TR-ARTICLE-1998-002
000114945 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000114945 970__ $$a0939.53042/GR-TR
000114945 980__ $$aARTICLE