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Affine rotation surfaces are a generalization of the well-known surfaces ofrevolution. Affine rotation surfaces arise naturally within the framework ofaffine differential geometry, a field started by Blaschke in the first decadesof the past century. Affine rotations are the affine equivalents of Euclideanrotations, and include certain shears as well as Euclidean rotations. Affinerotation surfaces are surfaces invariant under affine rotations. In this paper,we analyze several properties of algebraic affine rotation surfaces and, byusing some notions and results from affine differential geometry, we develop analgorithm for determining whether or not an algebraic surface given in implicitform, or in some cases in rational parametric form, is an affine rotationsurface. We also show how to find the axis of an affine rotation surface.Additionally, we discuss several properties of affine spheres, analogues ofEuclidean spheres in the context of affine differential geometry.

Affine differential geometry and affine rotation surfaces: algebraic surfaces invariant under non-Euclidean affine rotations