Holomorphic bi-disks in 9-dimensional CR hypersurfaces with Levi signature (2,2) must satisfy two complex torsion equations, and a concrete hypersurface is shown to violate one of them.
Canonical Cartan connection for $4$-dimensional CR-manifolds belonging to general class ${\sf II}$
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abstract
We study the equivalence problem for $4$-dimensional CR-manifolds of CR-dimension $1$ and codimension $2$ which are referred to as Engel CR-manifolds. We construct a canonical Cartan connection on such CR-manifolds through Cartan equivalence's method. In particular, we give the explicit expression of $4$ biholomorphic invariants, the annulation of which is a necessary and sufficient condition for an Engel manifold to be locally biholomorphic to Beloshapka's cubic in $\mathbb{C}^3$.
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math.DG 1years
2019 1verdicts
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Holomorphic immersions of bi-disks into $9$ dimensional real hypersurfaces with Levi signature $(2, 2)$
Holomorphic bi-disks in 9-dimensional CR hypersurfaces with Levi signature (2,2) must satisfy two complex torsion equations, and a concrete hypersurface is shown to violate one of them.