2019/03/18 by Thomas G. Brooks
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Codimension #Curvature #Diffeomorphism #Dimension (graph theory) #Elasticity and Material Modeling #Geometric Analysis and Curvature Flows #Geometry #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Ricci curvature #Riemann curvature tensor #Scalar curvature #Sectional curvature #math.DG #msc:53C20
paper · pdf · doi:10.1007/s10455-019-09678-5
12 pages, 1 figure
arxiv created 2019/03/18 · openalex publication_date 2019/08/08 · arxiv updated 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The conullity of a curvature tensor is the codimension of its kernel. We consider the cases of conullity two in any dimension and conullity three in dimension four. We show that these conditions are compatible with non-negative sectional curvature only if either the manifold is diffeomorphic to ℝn or the universal cover is an isometric product with a Euclidean factor. Moreover, we show that finite volume manifolds with conullity 3 are locally products.