Chern's conjecture (affine geometry)

Chern's conjecture in the context of affine geometry is a statement related to the existence of certain geometric structures and their properties. Specifically, it deals with the curvature of affine connections on manifolds. Chern, a prominent mathematician, formulated this conjecture in the realm of differential geometry, particularly focusing on affine differential geometry. Affine geometry studies properties that are invariant under affine transformations (i.e., transformations that preserve points, straight lines, and planes).