In mathematics, and especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. The term affine sphere is used because they play an analogous role in affine differential geometry to that of ordinary spheres in Euclidean differential geometry.
- All quadrics are affine spheres; the quadrics that are also improper affine spheres are the paraboloids.
- If ƒ is a smooth function on the plane and the determinant of the Hessian matrix is ±1 then the graph of ƒ in three-space is an improper affine sphere.
- E. V. Shikin. "Affine Sphere". Springer Online References.
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- Buchin, S. (1983). Affine differential geometry. Sci. Press and Gordon & Breach. ISBN 0-677-31060-9.
- Ishikawa, G.; Machida, Y. (2005). "Singularities of improper affine spheres and surfaces of constant Gaussian curvature". arXiv:math/0502154.
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