Six-dimensional totally nondegenerate CR submanifolds of C^5 are divided into fourteen branches with normal forms and automorphism algebras claimed, twelve complete, one partial, and one deferred.
Cartan equivalences for 5-dimensional CR-manifolds in C^4 belonging to General Class III_1
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abstract
We reduce to various absolute parallelisms, namely to certain {e}-structures on manifolds of dimensions 7, 6, 5, the biholomorphic equivalence problem or the intrinsic CR equivalence problem for generic submanifolds M^5 in C^4 of CR dimension 1 and of codimension 3 that are maximally minimal and are geometry-preserving deformations of one natural cubic model of Beloshapka, somewhere else called the General Class III-1 of 5-dimensional CR manifolds. Some inspiration links exist with the treatment of the General Class II previously done in 2007 by Beloshapka, Ezhov, Schmalz, and also with the classification of nilpotent Lie algebras due to Goze, Khakimdjanov, Remm.
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Holomorphic normal forms of six-dimensional totally nondegenerate CR manifolds in C^5
Six-dimensional totally nondegenerate CR submanifolds of C^5 are divided into fourteen branches with normal forms and automorphism algebras claimed, twelve complete, one partial, and one deferred.