Invariant conformal Killing forms on almost abelian Lie groups

2024/02/14 by Cecilia Herrera, Herrera, Cecilia, Marcos Origlia +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2402.09229

openalex publication_date 2024/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe completely conformal Killing or conformal Killing-Yano (CKY) p-forms on almost abelian metric Lie algebras. In particular we prove that if a n-dimensional almost abelian metric Lie algebra admits a non-parallel CKY p-form, then p=1 or p=n-1. In other words, any CKY p-form on a metric almost abelian Lie algebra is parallel for 2≤ p≤ n-2. Moreover, we characterize almost abelian Lie algebras admitting non-parallel CKY p-forms, and 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.

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