English Explanatory Dictionary

affine differential geometry

English dictionary entry

Meanings

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

Word forms

affine differential geometry

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.)

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