2007/09/30 by Mohammed Larbi Labbi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #gr-qc #math-ph #math.DG #math.MP #msc:53C20 #msc:53C25
paper · pdf · doi:10.3842/sigma.2007.118
published as SIGMA 3:118,2007 · This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2007/12/11 · openalex publication_date 2007/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The (2k)-th Gauss-Bonnet curvature is a generalization to higher dimensions of the (2k)-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for k =1. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.