Cayley surface

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An algebraic ruled surface which is a translation surface with an $\infty^1$ translation net. Its equation in Cartesian coordinates is


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.


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