  We discuss the sensitivity of fission barrier for heavy neutron-rich nuclei
to fission paths in the two dimensional neutron-proton quadrupole plane. To
this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine
the difference of fission barriers obtained with three constraining operators,
that is, the neutron, proton, and mass quadrupole operators. We investigate
$^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uranium
isotopes, that is relevant to r-process nucleosynthesis. We find that the
fission barrier heights are almost the same among the three constraining
operators even for neutron-rich nuclei, indicating that the usual way to
calculate fission barriers with the mass quadrupole operator is well justified.
We also discuss the difference between proton and neutron deformation
parameters along the fission paths.
