Gaussian Minkowski functionals (GMFs) for reasonably smooth subsets of Euclidean spaces, are defined as coefficients appearing in the the
Gaussian-tube-formula in finite dimensional Euclidean spaces. The fact that the measure in consideration here is Gaussian, itself makes the whole
analysis an infinite dimensional one. Therefore, one might want to generalize the definition of Gaussian Minkowski functionals to the subsets
of Wiener space which arise from reasonably smooth (in Malliavin sense) Wiener functionals. As in the finite dimensional case, we shall identify
the GMFs in the infinite dimensional case, as the coefficients appearing in the tube formula in Wiener space. Finally, we shall try to apply this
infinite dimensional generalization to get results about the geometry of excursion sets of a reasonably large class of random fields defined on a
"smooth" manifold.