Year: 2025
Type: article
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 $$\mathbb C^4$$ C 4 .
Source: Journal of Geometric Analysis
Authors: Boris Kruglikov, Andrea Santi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funders: Universitetet i Tromsø, Istituto Nazionale di Alta Matematica "Francesco Severi", Tromsø Forskningsstiftelse, Ministero dell’Istruzione, dell’Università e della Ricerca, Università degli Studi di Roma Tor Vergata, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, Norway Grants
OpenAlex ID: W4415526133