The Enneper surfaces are a three-parameter family of surfaces with constant negative curvature (and nonconstant mean curvature). In general, they are described by elliptic functions. However, a special case which can be specified parametrically using elementary functions is the Kuen surface.
Enneper's Negative Curvature Surfaces
See also
Kuen SurfaceExplore with Wolfram|Alpha
References
Enneper, A. "Analytisch-geometrische Untersuchungen." Nachr. Königl. Gesell. Wissensch. Georg-Augustus-Univ. Göttingen 12, 258-277, 1868.Fischer, G. (Ed.). Plate 92 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig, Germany: Vieweg, p. 88, 1986.Reckziegel, H. "Enneper's Surfaces." §3.4.4 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 37-39, 1986.Referenced on Wolfram|Alpha
Enneper's Negative Curvature SurfacesCite this as:
Weisstein, Eric W. "Enneper's Negative Curvature Surfaces." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EnnepersNegativeCurvatureSurfaces.html