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<p>This paper presents homogeneous CR hypersurfaces satisfying the <i>CR</i>-invariant property of being <i>k</i>-nondegenerate for an arbitrary integer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k\ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. The construction of such homogeneous manifolds is based on <i>CR</i> algebras defined by irreducible representations of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {su}(2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="fraktur">su</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. An explicit study of the iterated Levi forms with their respective kernels, along with the local model equation, is given.</p>

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On homogeneous CR manifolds of arbitrary order of Levi nondegeneracy

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Stefano Marini,
  • Costantino Medori

摘要

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