Affine $3$-spheres with constant affine curvature

Survey on Affine Spheres

Affine spheres were introduced by Ţiţeica in [72, 73], and studied later by Blaschke, Calabi, and Cheng-Yau, among others. These are hypersurfaces in affine R which are related to real Monge-Ampère equations, to projective structures on manifolds, and to the geometry of Calabi-Yau manifolds. In this survey article, we will outline the theory of affine spheres their relationships to these topics...

Affine Lines in Spheres

Because of the hairy ball theorem, the only closed 2-manifold that supports a lattice in its tangent space is T . But, if singular points (i.e. points whose tangent space is not endowed with 2 distinct coordinate directions) are allowed, then it becomes possible to give the tangent space a lattice. Because the lattice is well defined everywhere around the points, the effect of moving around the...

Scale-spaces and Affine Curvature

We present a new way to compute the aane curvature of plane curves. We explain how an aane scale-space can be used to gain one order of derivation in the numerical approximation of aane curvature. We outline our implementation and compare our results with previous ones. This paper ends by showing a simple application in pattern recognition using aane curvature.

Ricci curvature of affine connections

We show various examples of torsion-free affine connections which preserve volume elements and have definite Ricci curvature tensors.

Affine Spheres: Discretization via Duality Relations