A surface the affine normals (cf. Affine normal) of which intersect at one point. An affine sphere is said to be improper if this point is infinitely distant (or improper (ideal)); otherwise it is proper. In particular, any surface of the second order is an affine sphere. An improper convex affine sphere is an elliptic paraboloid.
Affine sphere. E.V. Shikin (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_sphere&oldid=13589