General affine differential geometry of surfaces in affine space $A^3$, I: the elliptical case

Abstract

In this paper we study the general affine differential geometry of surfaces in affine space $A^3$. 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.

20 pages. arXiv admin note: text overlap with arXiv:1603.03140 by other authors