Affine sphere

An affine sphere is a concept from differential geometry that relates to a certain class of surfaces in affine geometry. Specifically, an affine sphere is a surface in an affine space (a geometric setting that generalizes the properties of Euclidean spaces without the need for a fixed origin or notion of distance) that has the property that the one-parameter family of tangent planes at each point has a constant affine mean curvature. To elaborate, the affine mean curvature is a measure of how the surface bends in space.