The equivalence problem for 5-dimensional Levi degenerate CR manifolds

2012/10/20 by Medori, Costantino, Spiro, Andrea · 1 citation
#32V05 #32V40 #53C10 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.5638

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 is greater than or equal to 5 and if dim M = 5, then k= 2 at all points. We prove that for any 5-dimensional, uniformly 2-nondegenerate CR manifold M there exists a canonical Cartan connection, modelled on a suitable projective completion of the tube over the future light cone z∈ C³: (x¹)²+(x²)²-(x³)² = 0, x³>0. This determines a complete solution to the equivalence problem for this class of CR manifolds.

Cited by

• On Homogeneous CR Manifolds of Arbitrary Order of Levi Nondegeneracy

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