affine differential geometry

== English == === Etymology === The term reflects the categorisation developed by German mathematician Felix Klein for his Erlangen programme (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 === affine differential geometry (uncountable) (differential geometry) A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations. 1999, Alexander I. Bobenko, Wolfgang K. Schief, 5: Discrete Indefinite Affine Spheres, Alexander I. Bobenko, Ruedi Seiler (editors), Discrete Integrable Geometry and Physics, Oxford University Press (Clarendon Press), page 113, Tzitzeica'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. ==== Translations ==== === Further reading === Affine geometry on Wikipedia.Wikipedia Erlangen program on Wikipedia.Wikipedia Differential invariant on Wikipedia.Wikipedia Differential form on Wikipedia.Wikipedia Volume form on Wikipedia.Wikipedia