2012/03/11 by Daniel Clarke, Daniel J. Clarke, Clarke, Daniel J.
Mathematics · Physics and Astronomy · #53A20 (Primary) 53A15 #53A30 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.DG #msc:53A15 #msc:53A20 #msc:53A30
paper · pdf · doi:10.48550/arxiv.1203.2318
18 pages
openalex publication_date 2012/03/11 · arxiv created 2012/11/15 · arxiv updated 2012/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I give a theory of Moebius-flat hypersurfaces in n-dimensional projective space, analogous to that in conformal geometry. This unifies the classes of hypersurfaces with flat induced conformal structure (n > 3) and a classically studied class of surfaces (n = 3). I extend an example of Akivis-Konnov, and use polynomial conserved quantities to characterise hypersurfaces with flat centro-affine metric among Moebius-flat hypersurfaces. The theory has an obvious counterpart in Lie sphere geometry.