Difference between revisions of "Cayley surface"
From Encyclopedia of Mathematics
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| − | An algebraic ruled surface which is a translation surface with an | + | {{TEX|done}} |
| + | An algebraic [[ruled surface]] which is a translation surface with an $\infty^1$ translation net. Its equation in Cartesian coordinates is | ||
| − | + | $$x^3-6xy+6z=0.$$ | |
| − | The surface is named after A. Cayley [[#References|[1]]], who considered it as a geometrical illustration of his investigations in the theory of pencils of binary quadratic | + | The surface is named after A. Cayley [[#References|[1]]], who considered it as a geometrical illustration of his investigations in the theory of pencils of [[binary quadratic form]]s. |
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A. Cayley, "A fourth memoir on quantics" , ''Collected mathematical papers'' , '''2''' , Cambridge Univ. Press (1889) pp. 513–526 (Philos. Trans. Royal Soc. London 148 (1858), 415–427)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> A. Cayley, "A fourth memoir on quantics" , ''Collected mathematical papers'' , '''2''' , Cambridge Univ. Press (1889) pp. 513–526 (Philos. Trans. Royal Soc. London 148 (1858), 415–427)</TD></TR> | ||
| + | <TR><TD valign="top">[2]</TD> <TD valign="top"> V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)</TD></TR> | ||
| + | </table> | ||
| + | |||
| + | [[Category:Algebraic geometry]] | ||
Latest revision as of 19:03, 11 October 2014
An algebraic ruled surface which is a translation surface with an $\infty^1$ translation net. Its equation in Cartesian coordinates is
$$x^3-6xy+6z=0.$$
The surface is named after A. Cayley [1], who considered it as a geometrical illustration of his investigations in the theory of pencils of binary quadratic forms.
References
| [1] | A. Cayley, "A fourth memoir on quantics" , Collected mathematical papers , 2 , Cambridge Univ. Press (1889) pp. 513–526 (Philos. Trans. Royal Soc. London 148 (1858), 415–427) |
| [2] | V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian) |
How to Cite This Entry:
Cayley surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cayley_surface&oldid=16562
Cayley surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cayley_surface&oldid=16562
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article