Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if dim M = 5 and if dim M = 5, then k= 2 at all points. We prove that for any five-dimensional, uniformly two-nondegenerate CR manifold M there exists a canonical Cartan connection, modeled on a suitable projective completion of the tube over the future light cone {z \in C^3 : (x_1)^2 + (x_2)^2 - (x_3)^2 = 0, x_3 > 0}. This determines a complete solution to the equivalence problem for this class of CR manifolds.

The Equivalence Problem for Five-dimensional Levi Degenerate CR Manifolds / C. Medori; A. Spiro. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 20:(2014), pp. 5602-5647. [10.1093/imrn/rnt129]

### The Equivalence Problem for Five-dimensional Levi Degenerate CR Manifolds

#### Abstract

Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if dim M = 5 and if dim M = 5, then k= 2 at all points. We prove that for any five-dimensional, uniformly two-nondegenerate CR manifold M there exists a canonical Cartan connection, modeled on a suitable projective completion of the tube over the future light cone {z \in C^3 : (x_1)^2 + (x_2)^2 - (x_3)^2 = 0, x_3 > 0}. This determines a complete solution to the equivalence problem for this class of CR manifolds.
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The Equivalence Problem for Five-dimensional Levi Degenerate CR Manifolds / C. Medori; A. Spiro. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 20:(2014), pp. 5602-5647. [10.1093/imrn/rnt129]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2781130