Difference between revisions of "Adjoint surface"
From Encyclopedia of Mathematics
(Importing text file) |
m (links) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | A surface | + | {{TEX|done}} |
| + | A surface $Y$ that is in [[Peterson correspondence]] with a given surface $X$ and is, moreover, such that the [[asymptotic net]] on $Y$ corresponds to a conjugate net $\sigma$ on $X$ with equal invariants, and vice versa. The adjoint surface $Y$ is the [[rotation indicatrix]] for $X$, and vice versa. If $\sigma$ is a principal base for a [[Deformation over a principal base|deformation]] of $X$, then $Y$ is a [[Bianchi surface]]. | ||
| + | |||
| + | [[Category:Geometry]] | ||
Latest revision as of 19:44, 24 April 2016
A surface $Y$ that is in Peterson correspondence with a given surface $X$ and is, moreover, such that the asymptotic net on $Y$ corresponds to a conjugate net $\sigma$ on $X$ with equal invariants, and vice versa. The adjoint surface $Y$ is the rotation indicatrix for $X$, and vice versa. If $\sigma$ is a principal base for a deformation of $X$, then $Y$ is a Bianchi surface.
How to Cite This Entry:
Adjoint surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_surface&oldid=19305
Adjoint surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_surface&oldid=19305
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article