Handkerchief Surface

A surface given by the parametric equations

			(1)
			(2)
			(3)

The handkerchief surface has stationary points summarized in the table below, where the type of point can be found using the second derivative test.

			point
		48	local maximum
	4		saddle point

Its first fundamental form has coefficients

			(4)
			(5)
			(6)

and its second fundamental form has coefficients

			(7)
			(8)
			(9)

The Gaussian curvature can be given implicitly by

(10)