Cayley's ruled cubic surface

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

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

$z=xy-x^{3}/3\ .$

In projective coordinates it is $zw^{2}=xyw-x^{3}/3\$.

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

External links

• Cubical ruled surface
• Weisstein, Eric W. "Cayley Surface". MathWorld.