Catalan's Surface

A minimal surface given by the parametric equations

			(1)
			(2)
			(3)

(Gray 1997), or

			(4)
			(5)
			(6)

where

(7)

(do Carmo 1986).

The first fundamental form has coefficients

			(8)
			(9)
			(10)

and the second fundamental form has coefficients

			(11)
			(12)
			(13)

The principal curvatures are

			(14)
			(15)

the mean curvature is

(16)

and the Gaussian curvature is

(17)