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Cayley's ruled cubic surface

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Not to be confused with Cayley's nodal cubic surface.

In differential geometry, Cayley's ruled cubic surface is the ruled cubic surface

z = x y − x 3 / 3   . {\displaystyle z=xy-x^{3}/3\ .}

In projective coordinates it is z w 2 = x y w − x 3 / 3   {\displaystyle zw^{2}=xyw-x^{3}/3\ } .

It contains a (double) line of self-intersection x = w = 0   {\displaystyle x=w=0\ } and two pinch points.

References

  1. "Ruled Cubics | Mathematical Institute". www.maths.ox.ac.uk. Archived from the original on 2016-11-10. Retrieved 2020-08-08.

External links

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