affine differential geometry
nounEtymology
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.)
Definitions
A type of differential geometry in which the differential invariants studied are…
A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations.
- The basic difference between Riemannian and affine differential geometry is that in the affine case we introduce volume forms over a manifold instead of metrics.
The neighborhood
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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA