Conformal Killing Yano $2$-forms on Lie groups

Início: 21/10/2022 17:00

Término: 21/10/2022 18:00

Palestrante: Marcos Origlia (CONICET)

E-mail do Palestrante: marcosoriglia@gmail.com

Resumo: 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_Xmathrm{d}eta-dfrac{1}{n-p+1}X^*wedge mathrm{d}^*eta, ] where $X^{\ast }$ is the dual 1-form of $X$, $mathrm{d}^{\ast }$ is the codifferential, $nabla$ is the Levi-Civita connection associated to $g$ and $iot{a}_X$ is the interior product with $X$. If $eta$ is coclosed ($mathrm{d}^{\ast }eta=0$) 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.