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affine differential geometry

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

Noun

affine differential geometry (uncountable)

  1. (differential geometry) 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.
    • 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.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...

Examples of affine differential geometry in a sentence

  • The Tzitzeica surfaces are the analogues of spheres in affine differential geometry and, indeed, are known as affine spheres or affinsphären [39].2002, C. Rogers, W. K. Schief, Bäcklund and Darboux Transformations, Cambridge University Press, page 88:
  • In Chapter 4, we study questions related to real affine differential geometry.2012, Miguel Brozos-Vázquez, Peter B. Gilkey, Stana Nikcevic, Geometric Realizations of Curvature, World Scientific (Imperial College...

Origin of affine differential geometry

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.)

Questions about affine differential geometry

What does affine differential geometry mean?
Affine differential geometry means a type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations.
How do you use affine differential geometry in a sentence?
The Tzitzeica surfaces are the analogues of spheres in affine differential geometry and, indeed, are known as affine spheres or affinsphären [39].
What part of speech is affine differential geometry?
Affine differential geometry is a noun.

Words near affine differential geometry in the dictionary

  1. affine arithmetic
  2. affine combination
  3. affine combinations
  4. affine connection
  5. affine connections
  6. affine differential geometry
  7. affine geometries
  8. affine geometry
  9. affine group
  10. affine groups
  11. affine hull

Source and license

Adapted from Wiktionary: affine differential geometry (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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