Kuen Surface

The Kuen surface is a special case of Enneper's negative curvature surfaces which can be given parametrically by

			(1)
			(2)
			(3)
			(4)
			(5)

for , (Reckziegel et al. 1986; Gray et al. 2006, p. 484).

The Kuen surface appears on the cover of volume 2, number 1 of La Gaceta de la Real Sociedad Matemática Española (1999).

The coefficients of the first fundamental form are

			(6)
			(7)
			(8)

the second fundamental form coefficients are

			(9)
			(10)
			(11)

and the surface area element is

(12)

The Gaussian and mean curvatures are

			(13)
			(14)

so the Kuen surface has constant negative Gaussian curvature, and the principal curvatures are

			(15)
			(16)

(Gray 1997, p. 496).