On lightlike manifolds

Abstract

Our subject of study here is lightlike metrics o smooth manifolds, First a lightlike scalar product on vector space E is symmetric bilinear form b which is positive but nondefinite and which has exactly a 1-dimensional kernel. In this thesis we prove a rigidity of the lightcone in Minkowski space. it is essentially the unique space endowed with a lightlike metric and supporting an isometric nonproper action of semisimple lie group.