Generalized vector cross products and Killing forms on negatively curved manifolds

M.L. BARBERIS; ANDREI MOROIANU; UWE SEMMELMANN

GEOMETRIAE DEDICATA

SPRINGER

Lugar: Berlin; Año: 2020 vol. 205 p. 113 - 127

0046-5755

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 $nge 4$.