Affine differential geometry of osculating hypersurfaces

Lines and Osculating Lines of Hypersurfaces

This is a detailed study of the infinitesimal variation of the varieties of lines and osculating lines through a point of a low degree hypersurface in projective space. The motion is governed by a system of partial differential equations which we describe explicitly.

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...

Cheng and Yau’s Work on Affine Geometry and Maximal Hypersurfaces

As part of their great burst of activity in the late 1970s, Cheng and Yau proved many geometric results concerning differential structures invariant under affine transformations of R n. Affine differential geometry is the study of those differential properties of hypersurfaces in R n+1 which are invariant under volume-preserving affine transformations. One way to develop this theory is to start...

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.