Geometry of Centroaffine Surfaces in R⁵

2014/08/31 by Nathaniel Bushek, Jeanne N. Clelland
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Artificial intelligence #Class (philosophy) #Combinatorics #Computer science #Engineering #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Homogeneous #Mathematical analysis #Mathematics #Metric (unit) #Physics #Pure mathematics #Set (abstract data type) #math.DG

paper · pdf · doi:10.3842/sigma.2015.001

published as SIGMA 11 (2015), 001, 24 pages

arxiv created 2015/01/06 · openalex publication_date 2015/01/06 · arxiv updated 2015/01/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We use Cartan's method of moving frames to compute a complete set of local invariants for nondegenerate, 2-dimensional centroaffine surfaces in R 5 0 with nondegenerate centroaffine metric. We then give a complete classification of all homogeneous centroaffine surfaces in this class.

Citations

• Symmetric Bilinear Forms
• On Cartan’s method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry