General affine differential geometry of surfaces in affine space A³, I: the elliptical case

2018/04/15 by Xuan Zhao, Zhao, Xu-an, Hongzhu Gao +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1804.06250

openalex publication_date 2018/04/15 · openalex created_date 2018/04/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study the general affine differential geometry of surfaces in affine space A³. For a regular elliptical surface we define a moving frame of minimal order and get the complete system of differential invariants. As an application we classify regular elliptical surfaces of constant curvatures up to affine congruence.

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