A constant-curvature surface which can be given parametrically by
where
with
and
(Reckziegel 1986).
The coefficients of the first fundamental form
are
and the coefficients of the second fundamental
form are
The Sievert surface has Gaussian and mean
curvatures given by
Explore with Wolfram|Alpha
References
Fischer, G. (Ed.). Plate 87 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, p. 83, 1986.Gray, A. Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 499-500, 1997.Reckziegel, H. "Sievert's
Surface." §3.4.4.3 in Mathematical
Models from the Collections of Universities and Museums (Ed. G. Fischer).
Braunschweig, Germany: Vieweg, pp. 38-39, 1986.Sievert, H. Über
die Zentralflächen der Enneperschen Flachen konstanten Krümmungsmaßes.
Dissertation, Tübingen, 1886.
Cite this as:
Weisstein, Eric W. "Sievert's Surface."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SievertsSurface.html
Subject classifications