2016/11/07 by Marcos Salvai, Salvai, Marcos
Mathematics · Medicine · Physics and Astronomy · #53A15 #53A55 (Primary) 53A04 #53B30 (Secondary) #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1611.02347
openalex publication_date 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider smooth plane curves which are convex with respect to the origin.\nWe describe centro-affine invariants (that is, GL+(2,R)-invariants), such as\ncentro-affine curvature and arc length, in terms of the canonical Lorentz\nstructure on the three dimensional space of all the ellipses centered at zero,\nby means of null curves of osculating ellipses. This is the centro-affine\nanalogue of the approach to conformal invariants of curves in the sphere\nintroduced by Langevin and O'Hara, using the canonical pseudo Riemannian metric\non the space of circles.\n