affine differential geometry

短语

释义与例句

n.
  1. 1.

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

    不可数

    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.

    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.

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.)

来源：wiktionary