We investigate the problem of recognizing a generalization of surfaces of revolution appearing in the field of affine differential geometry, namely affine rotation surfaces. By using some notions from affine differential geometry, we determine how to detect whether or not a given implicit algebraic surface is an affine rotation surface. These results generalize some previous results of the authors on surfaces of revolution. As a by-product, we also provide an algorithm to detect whether or not an algebraic surface is an affine sphere, a generalization of Euclidean spheres of interest not only in geometry, but also in other fields.

中文翻译：

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识别代数仿射旋转曲面

我们研究了识别仿射微分几何领域中出现的旋转曲面，即仿射旋转曲面的泛化问题。通过使用仿射微分几何的一些概念，我们确定如何检测给定的隐式代数曲面是否是仿射旋转曲面。这些结果概括了作者在旋转表面上的一些先前结果。作为副产品，我们还提供了一种算法，用于检测代数曲面是否是仿射球体，即不仅在几何学上而且在其他领域中都对欧几里德球体感兴趣。