Meaning of affine differential geometry | Babel Free

Definitions

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

uncountable

Examples

“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.”

CEFR level