The branch of affine geometry that studies the invariants of an affine unimodular group of transformations. The most important fact is the existence in equi-affine geometry of areas of parallelograms in plane geometry and of volumes of parallelepipeds in three-dimensional geometry.


Comments

See [a1], p. 276; [a2], pp. 150-156; [a3], pp.40-52; [a4]; and [a5], p. 367.

References

[a1] M. Berger, "Geometry" , I , Springer (1987)
[a2] M. Spivak, "A comprehensive introduction to differential geometry" , 2 , Publish or Perish pp. 1–5
[a3] L. Fejes Toth, "Lagerungen in der Ebene, auf der Kugel und im Raum" , Springer (1972)
[a4] J. Dieudonné, "Treatise on analysis" , 4 , Acad. Press (1974)
[a5] W. Blaschke, "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , 2 , Springer (1923)
How to Cite This Entry:
Equi-affine geometry. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equi-affine_geometry&oldid=34173
This article was adapted from an original article by L.A. Sidorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article