Enneper surface

An algebraic minimal surface covering a surface of revolution. Its parametric equation is

$$ x = \frac{1}{4} ( u ^ {3} - 3 u - 3 u v ^ {2} ) , $$

$$ y = \frac{1}{4} ( 3 v + 3 u ^ {2} v - v ^ {3} ) , $$

$$ z = \frac{3}{4} ( v ^ {2} - u ^ {2} ) . $$

It was discovered by A. Enneper in 1864.

References

• [a1] J.C.C. Nitsche, "Vorlesungen über Minimalflächen", Springer (1975) Zbl 0319.53003