A surface of constant negative curvature obtained by twisting a pseudosphere and given by
the parametric equations

The above figure corresponds to , , , and .

Dini's surface is pictured in the upper right-hand corner of Gray (1997; left figure), as well as on the cover of volume 2, number 3 of La Gaceta de la Real Sociedad
Matemática Española (1999; right figure).

The coefficients of the first fundamental form
are

the coefficients of the second fundamental
form are

and the area element is

(10)

The Gaussian and mean
curvatures are given by

See also Pseudosphere
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References Geometry Center. "Dini's Surface." http://www.geom.umn.edu/zoo/diffgeom/surfspace/dini/ . Gray, A. "Dini's Surface." §21.5 in Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 493-495, 1997. Nordstrand, T. "Dini's
Surface." http://jalape.no/math/dintxt .
Cite this as:
Weisstein, Eric W. "Dini's Surface." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/DinisSurface.html

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