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

Maks A. Akivis·Vladislav V. Goldberg
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Abstract

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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Maks A. Akivis, Vladislav V. Goldberg. 1999-02-24. Lightlike hypersurfaces on a four-dimensional manifold endowed with a pseudoconformal structure of signature (2, 2). https://arxiv.org/abs/math/9902140

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