2018/06/16 by Maria Laura Barberis, María Laura Barberis, Andrei Moroianu +1 · 1 citation
Mathematics · #Algebraic geometry #Cross-ratio #Differential geometry #Dimension (graph theory) #Geometric Analysis and Curvature Flows #Killing vector field #Manifold (fluid mechanics) #Minimal volume #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Projective geometry #Riemannian manifold #Sectional curvature #math.DG
paper · pdf · doi:10.1007/s10711-019-00467-9
published as Geometriae Dedicata 205 (1), 113-127 (2020) · 16 pages
arxiv created 2018/06/16 · openalex created_date 2018/06/21 · openalex publication_date 2019/07/08 · arxiv updated 2021/06/15 · openalex updated_date 2026/08/05
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 ℝn and give their classification. Using previous results about Killing tensors on negatively curved manifolds and a new characterization of 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≥ 4.