Submaximally symmetric CR-structures

2015/09/21 by Kruglikov, Boris
#32M25 #32V20 #57S20 #58J70 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.06405

Abstract

Hypersurface type CR-structures with non-degenerate Levi form on a manifold of dimension (2n+1) have maximal symmetry dimension n²+4n+3. We prove that the next (submaximal) possible dimension for a (local) symmetry algebra is n²+4 for Levi-indefinite structures and n²+3 for Levi-definite structures when n>1. In the exceptional case of CR-dimension n=1, the submaximal symmetry dimension 3 was computed by E. Cartan.

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