Variations on Gromov's open-dense orbit theorem

Abstract

We investigate under which conditions a geometric structure which is locally homogeneous on a dense open set is locally homogeneous everywhere. In the case of 3-dimensional Lorentz metric, this allows us to sharpen the conclusions in Gromov's open-dense orbit theorem. Resume.-NousetudionsNousetudions sous quelles conditions une structure geometrique qui est localement homogene sur un ouvert dense est localement homogene partout. Dans la cadre des varietes lorentziennes de dimension 3, cela conduitaconduita un renforcement des conclusions dans le theoreme de l'orbite dense-ouverte de Gromov.