## Uniformly Levi degenerate CR manifolds: The 5-dimensional case.(English)Zbl 1020.32029

The problem studied in this paper is the existence of a CR diffeomorphism between two germs $$(M,p)$$ and $$(M',p')$$ of CR manifolds of hypersurface type. That question has already been solved for germs with a nondegenerate Levi form, and the author investigates here the case of 5-dimensional germs of hypersurface type with a degenerate Levi form of constant rank 1. Under a non-degeneracy condition he associates to any such germ $$(M,p)$$ a bundle $$Y\to M$$ and a 1-form $$\omega$$ on $$Y$$ with value in $$\mathbb{R}^{\dim Y}$$ giving an absolute parallelism on $$Y$$, and he proves that two germs $$(M,p)$$ and $$(M',p')$$ are CR equivalent if and only if the associated pairs $$(Y,\omega)$$ and $$(Y',\omega')$$ are isomorphic.
Using this theorem he gives a unique continuation principle for CR mappings between two such germs and characterizes the germs isomorphic to the tube over the light cone in $$\mathbb{R}^3$$.

### MSC:

 32V20 Analysis on CR manifolds 32V05 CR structures, CR operators, and generalizations 32V40 Real submanifolds in complex manifolds
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### References:

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