Catalan's minimal surface is minimal surface given
by the parametric equations
(Gray 1997), or
where
|
(7)
|
(do Carmo 1986).
The first fundamental form has coefficients
and the second fundamental form has coefficients
The principal curvatures are
the mean curvature is
|
(16)
|
and the Gaussian curvature is
|
(17)
|
See also
Catalan Ruled Surface
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References
Catalan, E. "Mémoire sur les surfaces dont les rayons de courbures en chaque point, sont égaux et les signes contraires."
Comptes Rendus Acad. Sci. Paris 41, 1019-1023, 1855.do
Carmo, M. P. "Catalan's Surface" §3.5D in Mathematical
Models from the Collections of Universities and Museums (Ed. G. Fischer).
Braunschweig, Germany: Vieweg, pp. 45-46, 1986.Fischer, G. (Ed.).
Plates 94-95 in Mathematische
Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, pp. 90-91, 1986.Gray, A. "Catalan's Minimal
Surface." Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 692-693, 1997.JavaView. "Classic
Surfaces from Differential Geometry: Catalan Surface." http://www-sfb288.math.tu-berlin.de/vgp/javaview/demo/surface/common/PaSurface_Catalan.html.
Cite this as:
Weisstein, Eric W. "Catalan Minimal Surface."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalanMinimalSurface.html
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