Effective Cartan-Tanaka connections for \(\mathcal C^6\)-smooth strongly pseudoconvex hypersurfaces \(M^3 \subset \mathbb C^2\) (Q639616)
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scientific article; zbMATH DE number 5949150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Effective Cartan-Tanaka connections for \(\mathcal C^6\)-smooth strongly pseudoconvex hypersurfaces \(M^3 \subset \mathbb C^2\) |
scientific article; zbMATH DE number 5949150 |
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Effective Cartan-Tanaka connections for \(\mathcal C^6\)-smooth strongly pseudoconvex hypersurfaces \(M^3 \subset \mathbb C^2\) (English)
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22 September 2011
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The Cartan curvature for the Tanaka connection of \(3\)-dimensional pseudoconvex hypersurfaces in \(\mathbb{C}^2\) are explicitly computed in terms of the \(6\)-th order jet of a defining function. It is shown that the vanishing of the curvature corresponds to bi-holomorphic equivalence to the sphere.
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Cartan connection
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Cartan curvature
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pseudoconvex hypersurface
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