2007/06/15 by Evgeny Volkov
Mathematics · #Analytic and geometric function theory #Characterization (materials science) #Closed set #Dimension (graph theory) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Harmonic #Honour #Manifold (fluid mechanics) #Metric (unit) #Riemannian manifold #math.DG
paper · pdf · doi:10.1112/jtopol/jtn014
8 pages
arxiv created 2007/06/15 · openalex publication_date 2008/06/09 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let M be a closed oriented manifold of dimension n and ω a closed 1-form on M. We discuss the question of whether there exists a Riemannian metric for which ω is co-closed. For closed 1-forms with nondegenerate zeros, the question was answered completely by Calabi in 1969; (cf. Calabi, Global analysis, Papers in honour of K. Kodaira). The goal of this paper is to give an answer in the general case, that is, without making any assumptions on the zero set of ω.