Eigenvalue pinching on spinc manifolds

2016/04/30 by Saskia Roos
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Convergence (economics) #Curvature #Eigenvalues and eigenvectors #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical physics #Mathematics #Metric (unit) #Physics #Pure mathematics #Quantum mechanics #Spin (aerodynamics) #Spinor #math.DG #math.SP

paper · pdf · doi:10.1016/j.geomphys.2016.11.006

28 pages, comments are welcome

openalex publication_date 2016/11/15 · arxiv created 2017/06/13 · arxiv updated 2017/06/14 · openalex created_date 2017/06/23 · openalex updated_date 2026/08/05

Abstract

We derive various pinching results for small Dirac eigenvalues using the classification of spin^c and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spin^c manifolds which involves a general study on convergence of Riemannian manifolds with a principal \mathbbS¹-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal \mathbbS¹-bundle on spin^c manifolds with Killing spinors.

Citations

• Some regularity theorems in riemannian geometry
• Riemannian Geometry of Contact and Symplectic Manifolds
• Multiple Integrals in the Calculus of Variations
• Manifolds with small Dirac eigenvalues are nilmanifolds
• Convergence and rigidity of manifolds under Ricci curvature bounds