Convergent normal forms for five dimensional totally nondegenerate CR manifolds in C^4
Abstract
Applying the equivariant moving frames method, we construct convergent normal forms for real-analytic 5-dimensional totally nondegenerate CR submanifolds of C^4. These CR manifolds are divided into several biholomorphically inequivalent subclasses, each of which has its own complete normal form. Moreover it is shown that, biholomorphically, Beloshapka's cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question.
Keywords
Cite
@article{arxiv.2004.11251,
title = {Convergent normal forms for five dimensional totally nondegenerate CR manifolds in C^4},
author = {Masoud Sabzevari},
journal= {arXiv preprint arXiv:2004.11251},
year = {2020}
}
Comments
As kindly noticed by Maria Stepanova, a computational error is found in the first version of the paper, concerning the computations of Branch 3-3-1 (Section 7.2.1). This error is corrected and the presentation is modified