affine differential geometry

Etymology
The term reflects the categorisation developed by German mathematician for his  (1872, Vergleichende Betrachtungen über neuere geometrische Forschungen), in which he found a useful distinction between projective, affine and Euclidean geometry (in order of increasing restrictiveness). (Riemannian geometry was not initially included.)

Noun

 * 1)  A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations.
 * 2) * 1999, Alexander I. Bobenko, Wolfgang K. Schief, 5: Discrete Indefinite Affine Spheres, Alexander I. Bobenko, Ruedi Seiler (editors), Discrete Integrable Geometry and Physics, (Clarendon Press), page 113,
 * 's classical papers are believed to have initiated a new area in mathematics, namely affine differential geometry.The present paper extends the above-mentioned approach to affine differential geometry.
 * 's classical papers are believed to have initiated a new area in mathematics, namely affine differential geometry.The present paper extends the above-mentioned approach to affine differential geometry.