Submaximally symmetric CR-structures

Boris Kruglikov

paper

Submaximally symmetric CR-structures

arXiv:1509.06405

Abstract

Hypersurface type CR-structures with non-degenerate Levi form on a manifold of dimension $(2 n + 1)$ have maximal symmetry dimension $n^{2} + 4 n + 3$ . We prove that the next (submaximal) possible dimension for a (local) symmetry algebra is $n^{2} + 4$ for Levi-indefinite structures and $n^{2} + 3$ 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.