1999/11/03 by Boris Botvinnik, Botvinnik, Boris, Brett McInnes +1 · 1 citation
Mathematics · Physics and Astronomy · #57R15 53C07 (53C80 81T13) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:53C07 #msc:57R15
paper · pdf · doi:10.48550/arxiv.math/9911023
13 pages, typos and minor corrections, conclusions unaffected
openalex publication_date 1999/11/03 · arxiv created 1999/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Witten and Yau (hep-th/9910245) have recently considered a generalisation of the AdS/CFT correspondence, and have shown that the relevant manifolds have certain physically desirable properties when the scalar curvature of the boundary is positive. It is natural to ask whether similar results hold when the scalar curvature is zero. With this motivation, we study compact scalar flat manifolds which do not accept a positive scalar curvature metric. We call these manifolds rigidly scalar-flat. We study this class of manifolds in terms of special holonomy groups. In particular, we prove that if, in addition, a rigidly scalar flat manifold M is Spin with dim M≥ 5, then M either has a finite cyclic fundamental group, or it must be a counter example to Gromov-Lawson-Rosenberg conjecture.