Canonical Cartan connection for $5$-dimensional CR-manifolds belonging to general class ${\sf III_2}$
Samuel Pocchiola
TL;DR
This paper constructs a canonical Cartan connection for 5-dimensional CR-manifolds of class III_2, providing a complete set of invariants to classify these manifolds up to biholomorphism.
Contribution
It introduces a canonical Cartan connection for a specific class of 5-dimensional CR-manifolds, enabling a systematic approach to their equivalence problem.
Findings
Constructed a 6-dimensional principal bundle for CR-manifolds of class III_2.
Developed a complete set of biholomorphic invariants for these manifolds.
Provided a method for classifying CR-manifolds in this class up to biholomorphism.
Abstract
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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Taxonomy
TopicsHolomorphic and Operator Theory · Geometric Analysis and Curvature Flows · Geometry and complex manifolds