the equation k is x1 x2 - y1 y2 = 1/4 in 4 space variables.
The surface lies on a sphere of radius 1 so x1^2+x2^2+y1^2+y2^2=1.
One cannot plot in 4 space so I wrote x1= r cos a, y1=r sin a,
x2= sqrt(1-r^2) cos b, y2= sqrt(1-r^2) sin b and plugged that in to get a function K(r,a b ) =1/4.
(Note that this reduces the number of variables to 3.)
My intention was then to take the r,a,b values from the implicit3d plot and plot3d those using
x1= r cos a, y1=r sin a,
x2= sqrt(1-r^2) cos b, y2= sqrt(1-r^2) sin b. Hence my question.
I say that I wanted to plot that but there is a simple workaround, namely
I project to R^3 stereographically via
x=x1/(1-y2), y=y1/)1-y2), z=2x2/(1-y2)
Then I can express k interms of x,y,z via s = x^2+y^2+z^2, x1= = 2x/(1+s), y1= = 2y/(1+s), y1= = 2z/(1+s), y2=( -1+x^2+y^2+z^2)/(1+s) to get an equation in K(x,y,z) = 1/4 and implicit3d plot that directly.
But since the issue came up I thought I'd ask.