Implicitization methods of
algebraic geometry can be used to find out that the points in the Enneper surface given above satisfy the degree-9
polynomial equation
Dually, the
tangent plane at the point with given parameters is where
Its coefficients satisfy the implicit degree-6 polynomial equation
It can be generalized to higher order rotational symmetries by using the Weierstrass–Enneper parameterization for integer k>1.[3] It can also be generalized to higher dimensions; Enneper-like surfaces are known to exist in for n up to 7.[7]
See also [8][9] for higher order algebraic Enneper surfaces.
References
^J.C.C. Nitsche, "Vorlesungen über Minimalflächen", Springer (1975)
^E. Güler, The algebraic surfaces of the Enneper family of maximal surfaces in three dimensional Minkowski space. Axioms. 2022; 11(1):4.
https://doi.org/10.3390/axioms11010004
Implicitization methods of
algebraic geometry can be used to find out that the points in the Enneper surface given above satisfy the degree-9
polynomial equation
Dually, the
tangent plane at the point with given parameters is where
Its coefficients satisfy the implicit degree-6 polynomial equation
It can be generalized to higher order rotational symmetries by using the Weierstrass–Enneper parameterization for integer k>1.[3] It can also be generalized to higher dimensions; Enneper-like surfaces are known to exist in for n up to 7.[7]
See also [8][9] for higher order algebraic Enneper surfaces.
References
^J.C.C. Nitsche, "Vorlesungen über Minimalflächen", Springer (1975)
^E. Güler, The algebraic surfaces of the Enneper family of maximal surfaces in three dimensional Minkowski space. Axioms. 2022; 11(1):4.
https://doi.org/10.3390/axioms11010004