I have the following code:
M = Manifold(3, 'M')
X.<x,y,z> = M.chart()
N = Manifold(3, 'N')
XN.<a,b1,b2> = N.chart()
omega = N.diff_form(2)
omega[0,1] = 2*b2/a^3
omega[0,2] = -2*b1/a^3
omega[1,2] = -2/a^2
Then I define a map M to N.
r = sqrt(x^2+y^2+z^2)
t = var('t', domain='real')
STSa = r^(1/2)*(r*cosh(2*r*t) - z*sinh(2*r*t))^(-1/2)
STSb1 = (x*sinh(2*r*t)/r)*STSa
STSb2 = (y*sinh(2*r*t)/r)*STSa
STS = M.diffeomorphism(N, [STSa, STSb1, STSb2])
Finally, I attempt to compute the pullback of omega to M by the map STS:
s = STS.pullback(omega)
Unfortunately, the program runs and runs and nothing ever comes out. Can anyone identify the issue? Of course, the Jacobian of the map STS will not be very nice, but this pullback should be perfectly computable.
