Canonical Cartan connection for $5$-dimensional CR-manifolds belonging to general class ${\sf III_2}$

Samuel Pocchiola

Canonical Cartan connection for $5$-dimensional CR-manifolds belonging to general class ${\sf III_2}$

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arxiv 1405.1342 v1 pith:ZGWMTNGY submitted 2014-05-05 math.CV

Samuel Pocchiola This is my paper · ORCID

classification math.CV

keywords cr-manifoldsdimensionalbelongingcanonicalcartanclassconnectiongeneral

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We study the equivalence problem for CR-manifolds belonging to general class III_2, i.e. the 5-dimensional CR-manifolds of CR-dimension 1 and codimension 3 whose CR-bundle satisfies a certain degeneracy condition. For such a CR-manifold M, we construct a canonical Cartan connection on a 6-dimensional principal bundle P on M. This provides a complete set of biholomorphic invariants for M.

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Holomorphic immersions of bi-disks into $9$ dimensional real hypersurfaces with Levi signature $(2, 2)$
math.DG 2019-08 conditional novelty 6.0 of 10

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.

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