Semicanonical moving frame of the hypersurface in a unimodular 4-dimensional affine space
In this note, we are concerned with the Kozlowski-Simon conjecture on ovaloids and prove that it is correct under additional conditions.
We focus our attention on projectively flat affine surfaces. First, we classify the affine surfaces with projectively flat induced connection and constant Pick invariant. We also investigate the compact case and study how the geometry at the boundary determines the geometry of the surface.