Nonlinear Harmonic Forms and an Indefinite Bochner Formula

2014/11/01 by Mark Stern, Stern, Mark
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1411.0144

openalex publication_date 2014/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We introduce the study of nonlinear harmonic forms. These are forms which minimize the L₂ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence results. We also introduce a variant of the Bochner formula suitable for probing the structure of the intersection form of a 4-manifold.

Citations

• Harmonic Mappings of Riemannian Manifolds

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