On lightlike geometry: isometric actions,and rigidity aspects

Degenerate Riemannian metrics exist naturally in various contexts. Unfortunately, their study stops to the ‘admission of failure’ that they are too poor, for instance, to generate a coherent intrinsic or extrinsic differential geometry, e.g. a kind of Levi-Civita connection. In this first text, we start the investigation of rigidity aspects of these structures, from the point of view of isometric actions of ‘big’ (e.g. semi-simple) Lie groups. To cite this article: E. Bekkara et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).