# Cayley surface

From Encyclopedia of Mathematics

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=33552

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article