On Homogeneous CR Manifolds of Arbitrary Order of Levi Nondegeneracy

TL;DR

This paper constructs and analyzes homogeneous CR hypersurfaces that are k-nondegenerate for any integer k, using CR algebras derived from irreducible representations of su(2), and provides explicit local models and Levi form analysis.

Contribution

It introduces a method to construct homogeneous CR manifolds with arbitrary Levi nondegeneracy order using su(2) representations, expanding understanding of CR geometry.

Findings

Explicit models of k-nondegenerate homogeneous CR hypersurfaces

Detailed analysis of iterated Levi forms and kernels

Local model equations for these manifolds

Abstract

This paper present homogeneous CR hypersurfaces satisfying the $CR$-invariant property of being $k$-nondegenerate for an arbitrary integer $k\geq 1$. The construction of such homogeneous manifolds are based on $CR$ algebras defined by irreducible representations of $\mathfrak{su}(2)$. An explicit study of the iterated Levi forms with their respective kernels, along with the local model equation, is given.