This paper is divided into three parts. Part I develops a general, new theory (inspired by
modern CR geometry) of Lie symmetries of completely integrable pde systems, viewed from …

We study the local equivalence problem for five dimensional real hypersurfaces $ M^ 5$ of
$\mathbb {C}^ 3$ which are $2 $-nondegenerate and of constant Levi rank $1 $ under …

We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces
M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type …

Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-
equivalence, by E. Cartan. We classify, up to local CR-equivalence, all locally homogeneous …

We develop the Cartan equivalence problem for Levi-non-degenerate $\mathcal C^ 6$-
smooth real hypersurfaces $ M^ 3$ in $\mathbb C^ 2$ in great detail, performing all …

We explicitly determine the structure equations of 5-dimensional Levi 2-nondegenerate CR
hypersurfaces, using our recently constructed canonical Cartan connection for this class of …

We reduce to various absolute parallelisms, namely to certain {e\} e-structures on manifolds
of dimensions 7, 6, 5, the biholomorphic equivalence problem or the intrinsic CR …

We study the holomorphic equivalence problem for finite type hypersurfaces in C 2. We
discover a geometric condition, which is sufficient for the existence of a natural convergent …

Normal forms in Cauchy-Riemann geometry Page 162 Contemporary Mathematics Volume
681 , 2017 http://dx. doi. org/10.1090/conm/681/13685 Normal forms in Cauchy-Riemann …

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms
associated to three specific model real analytic CR-generic submanifolds in ℂ 9 by …