On 3-nondegenerate CR manifolds in dimension 7 (II): the intransitive case
Abstract
We investigate 3-nondegenerate CR structures in the lowest possible dimension 7 and show that 8 is the maximal dimension for the Lie algebra of symmetries of such structures. The next possible symmetry dimension is 6, and for the automorphism groups the dimension 7 is also realizable. This part (II) is devoted to the case where the symmetry algebra acts intransitively. We use various methods to bound its dimension and demonstrate the existence of infinitely many non-equivalent submaximally symmetric models. Summarizing, we get a stronger form of Beloshapka's conjecture on the symmetry dimension of hypersurfaces in .
Keywords
Cite
@article{arxiv.2308.02841,
title = {On 3-nondegenerate CR manifolds in dimension 7 (II): the intransitive case},
author = {Boris Kruglikov and Andrea Santi},
journal= {arXiv preprint arXiv:2308.02841},
year = {2025}
}
Comments
47 pages, v2: a finer form for the rational normal curves is provided (the previous one also works), acknowledgments are updated. Final version to appear on J. Geom. Anal. The supplementary files are not reproduced in this version, but they are equally relevant and can be accessed through v1