Structure equations of Levi degenerate CR hypersurfaces of uniform type

Abstract

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 CR manifolds. We also give an outline of the basic properties of absolute parallelisms and Cartan connections, together with a brief discussion of the absolute parallelisms for such CR manifolds existing in the literature.

23 pages; in the new version Sect.2 is slightly shorter; to appear on Rendiconti del Seminario Matematico-Università e Politecnico di Torino

References in corpus (2)

• Explicit absolute parallelism for $2$-nondegenerate real hypersurfaces $M^5\subset {\mathbb{C}}^3$ of constant Levi rank $1$
• The equivalence problem for 5-dimensional Levi degenerate CR manifolds

Cited by in corpus (3)

• Affine Rigidity Without Integration
• Normal Forms for Rigid ${\mathfrak{C}}_{2,1}$ Hypersurfaces $M^5\subset {\mathbb{C}}^3$
• On Convergent Poincaré-Moser Reduction for Levi Degenerate Embedded $5$-Dimensional CR Manifolds