Mathematics – Differential Geometry
Scientific paper
1999-02-24
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 $V$.
Akivis Maks A.
Goldberg Vladislav V.
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