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On Homogeneous CR Manifolds of Arbitrary Order of Levi Nondegeneracy (2506.00897v2)
Published 1 Jun 2025 in math.DG
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.