PreprintCC BY 4.0arXiv
Holomorphic normal forms of six-dimensional totally nondegenerate CR manifolds in C^5
Abstract
The class of six-dimensional totally nondegenerate CR submanifolds in ℂ5 contains an infinite number of models parameterized by nonzero pairs (a, b)∈ℂ×ℝ appearing in their defining equations. Employing the equivariant moving frame method, we construct normal forms of this class. The applied normalizations yield into fourteen biholomorphically inequivalent subclasses, each with its own normal form. For each subclass, we determine the Lie algebra of infinitesimal CR automorphisms. Finally, using the method of involution, we prove the convergence of the constructed normal forms.
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BibTeX
@misc{sabzevari2026holomorphic,
title = {{Holomorphic normal forms of six-dimensional totally nondegenerate CR manifolds in C^5}},
author = {Masoud Sabzevari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.00684},
eprint = {2608.00684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00684},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Holomorphic normal forms of six-dimensional totally nondegenerate CR manifolds in C^5
AU - Masoud Sabzevari
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2608.00684
UR - https://arxiv.org/abs/2608.00684
AB - The class of six-dimensional totally nondegenerate CR submanifolds in ℂ^5 contains an infinite number of models parameterized by nonzero pairs (a, b)∈ℂ×ℝ appearing in their defining equations. Employing the equivariant moving frame method, we construct normal forms of this class. The applied normalizations yield into fourteen biholomorphically inequivalent subclasses, each with its own normal form. For each subclass, we determine the Lie algebra of infinitesimal CR automorphisms. Finally, using the method of involution, we prove the convergence of the constructed normal forms.
ER -