affine differential geometry
Word Rarity
Very rare
Frequency: 2.40 in modern English
45
Scrabble Score
26
Letters
9
Syllables
13
Unique Chars
Meaning
noun
A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations.
Uncountable
Example Sentences
- "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."
- "The Tzitzeica surfaces are the analogues of spheres in affine differential geometry and, indeed, are known as affine spheres or affinsphären [39]. According to Nomizu and Sasaki [227], the origins of affine differential geometry reside in this work of Tzitzeica at the turn of the nineteenth century."
- "In Chapter 4, we study questions related to real affine differential geometry. The structure group in Riemannian geometry is the orthogonal group #92;mathcal#123;O#125;. The structure group in affine differential geometry is the affine group."
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.)