Lightlike hypersurfaces on a four-dimensional manifold endowed with a pseudoconformal structure of signature (2, 2)

Details Lightlike hypersurfaces on a four-dimensional manifold endowed with a pseudoconformal structure of signature (2, 2) Lightlike hypersurfaces on a four-dimensional manifold endowed with a pseudoconformal structure of signature (2, 2)

1999-02-24

arxiv.org/abs/math/9902140v1

Atti Congr Intern in honour of Pasquale Calapso (Messina, 1998), Palermo, 2000, pp. 159-190

Mathematics

Differential Geometry

LaTeX, 23 pages

Scientific paper

The authors study the geometry of lightlike hypersurfaces on a four-dimensional manifold $(M, c)$ endowed with a pseudoconformal structure $c = CO (2, 2)$. They prove that a lightlike hypersurface $V \subset (M, c)$ bears a foliation formed by conformally invariant isotropic geodesics and two isotropic distributions tangent to these geodesics, and that these two distributions are integrable if and only if $V$ is totally umbilical. The authors also indicate how, using singular points and singular submanifolds of a lightlike hypersurface $V \subset (M, c)$, to construct an invariant normalization of $V$ intrinsically connected with $V$.

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