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<p>We give a complete description of conformal Killing or conformal Killing–Yano (CKY) <i>p</i>-forms on almost abelian metric Lie algebras. In particular, we prove that if an <i>n</i>-dimensional almost abelian metric Lie algebra admits a non-parallel CKY <i>p</i>-form, then <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p=n-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. In other words, any CKY <i>p</i>-form on a metric almost abelian Lie algebra is parallel for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(2\le p\le n-2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. We determine all metric almost abelian Lie algebras of dimension 4 (up to isometry) admitting non-parallel CKY <i>p</i>-forms. Moreover, we classify all Lie algebras with this property up to dimension 5, distinguishing also those cases where the associated simply connected Lie group admits lattices.</p>

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Invariant conformal Killing forms on almost abelian Lie groups

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • A. C. Herrera,
  • M. Origlia

摘要

We give a complete description of conformal Killing or conformal Killing–Yano (CKY) p-forms on almost abelian metric Lie algebras. In particular, we prove that if an n-dimensional almost abelian metric Lie algebra admits a non-parallel CKY p-form, then \(p=1\) p = 1 or \(p=n-1\) p = n - 1 . In other words, any CKY p-form on a metric almost abelian Lie algebra is parallel for \(2\le p\le n-2\) 2 ≤ p ≤ n - 2 . We determine all metric almost abelian Lie algebras of dimension 4 (up to isometry) admitting non-parallel CKY p-forms. Moreover, we classify all Lie algebras with this property up to dimension 5, distinguishing also those cases where the associated simply connected Lie group admits lattices.