affine differential geometry

名词 n.
中文释义

英文释义

名词 n.
  1. A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations. uncountable
    — 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.

词源

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.)
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