Namespaces
Variants
Actions

Difference between revisions of "Centro-affine geometry"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
m (tex encoded by computer)
 
Line 1: Line 1:
The branch of [[Affine geometry|affine geometry]] in which one studies invariants of centro-affine transformations: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021300/c0213001.png" />. Centro-affine transformations leave one point (the centre) fixed. In centro-affine geometry there is complete duality: To every proposition concerning points corresponds the same proposition concerning hyperplanes.
+
<!--
 +
c0213001.png
 +
$#A+1 = 1 n = 0
 +
$#C+1 = 1 : ~/encyclopedia/old_files/data/C021/C.0201300 Centro\AAhaffine geometry
 +
Automatically converted into TeX, above some diagnostics.
 +
Please remove this comment and the {{TEX|auto}} line below,
 +
if TeX found to be correct.
 +
-->
 +
 
 +
{{TEX|auto}}
 +
{{TEX|done}}
 +
 
 +
The branch of [[Affine geometry|affine geometry]] in which one studies invariants of centro-affine transformations: $  \overline{x}\; {}  ^ {i} = A _ {s}  ^ {i} x  ^ {s} $.  
 +
Centro-affine transformations leave one point (the centre) fixed. In centro-affine geometry there is complete duality: To every proposition concerning points corresponds the same proposition concerning hyperplanes.

Latest revision as of 16:43, 4 June 2020


The branch of affine geometry in which one studies invariants of centro-affine transformations: $ \overline{x}\; {} ^ {i} = A _ {s} ^ {i} x ^ {s} $. Centro-affine transformations leave one point (the centre) fixed. In centro-affine geometry there is complete duality: To every proposition concerning points corresponds the same proposition concerning hyperplanes.

How to Cite This Entry:
Centro-affine geometry. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Centro-affine_geometry&oldid=46297
This article was adapted from an original article by L.A. Sidorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article