English

On 3-nondegenerate CR manifolds in dimension 7 (I): the transitive case

Complex Variables 2025-04-18 v3 Differential Geometry Representation Theory

Abstract

We investigate 3-nondegenerate CR structures in the lowest possible dimension 7, and one of our goals is to prove Beloshapka's conjecture on the symmetry dimension bound for hypersurfaces in C4\mathbb{C}^4. We claim that 8 is the maximal symmetry dimension of 3-nondegenerate CR structures in dimension 7, which is achieved on the homogeneous model. This part (I) is devoted to the homogeneous case: we prove that the model is locally the only homogeneous 3-nondegenerate CR structure in dimension 7.

Keywords

Cite

@article{arxiv.2302.04513,
  title  = {On 3-nondegenerate CR manifolds in dimension 7 (I): the transitive case},
  author = {Boris Kruglikov and Andrea Santi},
  journal= {arXiv preprint arXiv:2302.04513},
  year   = {2025}
}

Comments

40 pages, v3: Final version to appear on J. Reine Angew. Math. The supplementary files are not reproduced in this version, but they are equally relevant and can be accessed through v1