Henneberg surface

In differential geometry, the Henneberg surface is a non-orientable minimal surface named after Lebrecht Henneberg.

It has parametric equation

and can be expressed as an order-15 algebraic surface. It can be viewed as an immersion of a punctured projective plane. Up until 1981 it was the only known non-orientable minimal surface.

The surface contains a semicubical parabola ("Neile's parabola") and can be derived from solving the corresponding Björling problem.

References

Further reading

• E. Güler; Ö. Kişi; C. Konaxis, Implicit equations of the Henneberg-type minimal surface in the four-dimensional Euclidean space. Mathematics 6(12), (2018) 279. .
• E. Güler; V. Zambak, Henneberg's algebraic surfaces in Minkowski 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2), (2019) 1761–1773. .