The geometry of lightlike hypersurfaces on manifolds endowed with a conformal structure of Lorentzian signature

Maks A. Akivis and Vladislav V. Goldberg


Abstract. The authors study the geometry of lightlike hypersurfaces $V$ on a manifold $(M, c)$ endowed with a pseudoconformal structure $c$ of Lorentzian signature. They find singular points and singular submanifolds of $V$ and use them to construct a conformally invariant normalization of $V$ intrinsically connected with its geometry. This normalization is constructed by means of the elements of a fourth-order neighborhood of a point $x \in V$ and induces a torsion-free affine connection on $V$ which is also intrinsically connected with the geometry of $V$.

AMSclassification. 53A30, 53B25

Keywords. Pseudoconformal structure, Lorentzian signature, lightlike hypersurface, isotropic geodesics, singular point, invariant normalization, affine connection