Conformal Killing Yano $2$-forms on Lie groups

Abstract: A differential $p$-form $\eta$ on a $n$-dimensional Riemannian manifold $(M,g)$ is called Conformal Killing Yano (CKY for short) if it satisfies for any vector field $X$ the following equation $$\nabla_X \eta=\dfrac{1}{p+1}\iota_X\mathrm{d}\eta-\dfrac{1}{n-p+1}X^*\wedge \mathrm{d}^*\eta,$$ where $X^*$ is the dual 1-form of $X$, $\mathrm{d}^*$ is the codifferential, $\nabla$ is the Levi-Civita connection associated to $g$ and $\iota_X$ is the interior product with $X$. If $\eta$ is coclosed ($\mathrm d^*\eta=0$) then $\eta$ is said to be a Killing-Yano $p$-form (KY for short).

We study left invariant Conformal Killing Yano $2$-forms on Lie groups endowed with a left invariant metric. We determine, up to isometry, all $5$-dimensional metric Lie algebras under certain conditions, admitting a CKY $2$-form. Moreover, a characterization of all possible CKY tensors on those metric Lie algebras is exhibited.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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