  Invariant manifolds play an important role in the study of the qualitative
dynamical behaviors for nonlinear stochastic partial differential equations.
However, the geometric shape of these manifolds is largely unclear. The purpose
of the present paper is to try to describe the geometric shape of invariant
manifolds for a class of stochastic partial differential equations with
multiplicative white noises. The local geometric shape of invariant manifolds
is approximated, which holds with significant likelihood. Furthermore, the
result is compared with that for the corresponding deterministic partial
differential equations.
