Affine differential geometry of surfaces

Differential Invariants of Equi–Affine Surfaces

We show that the algebra of equi-affine differential invariants of a suitably generic surface S ⊂ R is entirely generated by the third order Pick invariant via invariant differentiation. The proof is based on the new, equivariant approach to the method of moving frames. The goal of this paper is to prove that, in three-dimensional equi-affine geometry, all higher order differential invariants o...

Computational Geometry from the Viewpoint of Affine Differential Geometry

Recent research in Affine Differential Geometry

In this paper we emphasize the geometry of affine immersions, widely developed in recent years. Mathematics Subject Classification: 01-02, 01A65.

Affine geometry of surfaces and hypersurfaces in R

In the following we will give an overview of our research area. Most of it belongs to the field of affine differential geometry. Geometry, as defined in Felix Klein’s Erlanger Programm, is the theory of invariants with respect to a given transformation group. In this sense affine geometry corresponds to the affine group (general linear transformations and translations) and it’s subgroups acting...

Affine Mappings of Translation Surfaces: Geometry and Arithmetic

1. Introduction. Translation surfaces naturally arise in the study of billiards in rational polygons (see [ZKa]). To any such polygon P , there corresponds a unique translation surface, S = S(P), such that the billiard flow in P is equivalent to the geodesic flow on S (see, e.g., [Gu2], [Gu3]). There is also a classical relation between translation surfaces and quadratic differentials on a Riem...