Abstract
Let be Cayley’s ruled cubic surface in a projective three-space over any commutative field . We determine all collineations fixing , as a set, and all cubic forms defining . For both problems the cases turn out to be exceptional. On the other hand, if then the set of simple points of 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.
Citation
Johannes Gmainer. Hans Havlicek. "Isometries and collineations of the Cayley surface." Innov. Incidence Geom. 2 109 - 127, 2005. https://doi.org/10.2140/iig.2005.2.109
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