2024/02/28 by Julien Heyd, Heyd, Julien, Joël Merker +1
Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2402.18437
openalex publication_date 2024/02/28 · openalex created_date 2024/03/05 · openalex updated_date 2026/07/28
We determine all affinely homogeneous models for surfaces S2 ⊂ ℝ4, including the simply transitive models. We employ an improved power series method of equivalence, which captures invariants at the origin, creates branches, and infinitesimalizes calculations. We find several inequivalent terminal branches yielding each to some nonempty moduli space of homogeneous models, sometimes parametrized by a certain invariant algebraic variety. Three main features may be emphasized: 1) Iterated single-pointed jet bundles; 2) Cartan-enhanced power series method of equivalence; 3) Constant ping-pong between normal forms (nf) and vector fields (vf).