This metric arises from a parameterization of the five sphere x21 + x22 + x23 +...+ x26 = 1 and anti-de-Sitter space - y2-1- y20 +y21 + y22 + ...y24 = -1 through
if if if x1 + ix2 = sing cosy e 1, x3 + ix4 = sing siny e 2, x5 +ix6 = cosg e 3; y1 + iy2 = sinhr cosyeif1, y3 + iy4 = sinh r siny eif2, y-1 + iy0 = coshr eit.
The embedding coordinates Xm(t, s) and Y m(t,s) in (4View Equation) are hence given by Xm = (r,y,f1,f2,t) and Y m = (g,y,f1,f2,f3).