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 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.
Kruglikov, B., Santi, A. (2025). On 3-nondegenerate 7-dimensional CR manifolds (I): the transitive case. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK [10.1515/crelle-2024-0093].
On 3-nondegenerate 7-dimensional CR manifolds (I): the transitive case
Santi, Andrea
2025-01-08
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 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.| File | Dimensione | Formato | |
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On 3-nondegenerate CR manifolds in dimension 7 (I) The transitive case.pdf
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