affine differential geometry

Meaning

Noun

• A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations.

Origin

• 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.)