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arXiv · 1304.0230

Isometries and Collineations of the Cayley Surface

Johannes Gmainer·Hans Havlicek
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Abstract

Let $F$ be Cayley's ruled cubic surface in a projective three-space over any commutative field $K$. We determine all collineations fixing $F$, as a set, and all cubic forms defining $F$. For both problems the cases $|K|=2,3$ turn out to be exceptional. On the other hand, if $|K|\geq 4$ then the set of simple points of $F$ can be endowed with a non-symmetric distance function. We describe the corresponding circles, and we establish that each isometry extends to a unique projective collineation of the ambient space.

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Johannes Gmainer, Hans Havlicek. 2013-03-31. Isometries and Collineations of the Cayley Surface. https://arxiv.org/abs/1304.0230

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