A characterization of hyperbolic affine flat, affine minimal surfaces in \mathbbA³

2013/08/01 by Jeanne N. Clelland, Jonah Miller, Jonah M. Miller +2
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications #Primary(53A15) #Secondary(58A15) #math.DG

paper · pdf · doi:10.48550/arxiv.1308.0288

15 pages

arxiv created 2013/08/01 · openalex publication_date 2013/08/01 · arxiv updated 2013/08/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We investigate the geometric properties of hyperbolic affine flat, affine minimal surfaces in the equiaffine space \mathbbA³. We use Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a complete local classification of such surfaces and construct new examples.

Related

• General affine differential geometry of surfaces in affine space A³, I: the elliptical case
• The geometry of locally symmetric affine surfaces
• Hyperbolic surfaces in \bf P³: examples
• Geometry of [φ,e₃]-minimal surfaces in ℝ³
• Minimal surfaces in germs of hyperbolic 3--manifolds