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.
How to Cite This Entry:
Affine sphere. E.V. Shikin (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_sphere&oldid=13589
Affine sphere. E.V. Shikin (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_sphere&oldid=13589
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098