Courbes et hypersurfaces nulles en géométrie pseudo-Riemannienne

Abstract : In this thesis, we study "degenerate" (or "null") submanifolds of pseudo-riemannian manifolds, for which the restriction of the pseudo-riemannian structure of the ambiant manifold degenerate on the submanifold. In the first part, we build a generalized Frénet 's frame in pseudo-riemannian manifolds. In the second part, we generalize our construction to other situations, such as symplectic manifolds, or pseudo-kaehlerian manifolds. Finally, in the last part of this thesis, we study totally geodesic degenerate hypersurfaces in pseudo-riemannian manifolds. We find invariants relative to the induced structure on the hypersurface, and use them to build local coordinate systems adapted to the geometry of the hypersurface.
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Xavier Charuel. Courbes et hypersurfaces nulles en géométrie pseudo-Riemannienne. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2003. Français. ⟨NNT : 2003NAN10005⟩. ⟨tel-01754437⟩

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