Difference between revisions of "Equi-affine geometry"
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The branch of [[Affine geometry|affine geometry]] that studies the invariants of an [[Affine unimodular group|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. | The branch of [[Affine geometry|affine geometry]] that studies the invariants of an [[Affine unimodular group|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. | ||
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''I''' , Springer (1987)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Spivak, "A comprehensive introduction to differential geometry" , '''2''' , Publish or Perish pp. 1–5</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> L. Fejes Toth, "Lagerungen in der Ebene, auf der Kugel und im Raum" , Springer (1972)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top"> J. Dieudonné, "Treatise on analysis" , '''4''' , Acad. Press (1974)</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> W. Blaschke, "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , '''2''' , Springer (1923)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''I''' , Springer (1987)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Spivak, "A comprehensive introduction to differential geometry" , '''2''' , Publish or Perish pp. 1–5</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> L. Fejes Toth, "Lagerungen in der Ebene, auf der Kugel und im Raum" , Springer (1972)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top"> J. Dieudonné, "Treatise on analysis" , '''4''' , Acad. Press (1974)</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> W. Blaschke, "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , '''2''' , Springer (1923)</TD></TR></table> | ||
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Latest revision as of 21:14, 1 November 2014
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=16433
Equi-affine geometry. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equi-affine_geometry&oldid=16433
This article was adapted from an original article by L.A. Sidorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article