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arXiv · 1806.06255

Generalized vector cross products and Killing forms on negatively curved manifolds

Maria Laura Barberis·Andrei Moroianu·Uwe Semmelmann
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Abstract

Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using previous results about Killing tensors on negatively curved manifolds and a new characterization of $\mathrm{SU}(3)$-structures in dimension $6$ whose associated $3$-form is Killing, we then show that every Killing $3$-form on a compact $n$-dimensional Riemannian manifold with negative sectional curvature vanishes if $n\ge 4$.

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Maria Laura Barberis, Andrei Moroianu, Uwe Semmelmann. 2018-06-16. Generalized vector cross products and Killing forms on negatively curved manifolds. https://doi.org/10.1007/s10711-019-00467-9

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