  Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold
without boundary. In this paper, we generalize nonwindowed geometric scattering
transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ norms of a
cascade of geometric wavelet transforms and modulus operators. We then provide
weighted measures for these operators, prove that these operators are
well-defined under specific conditions on the manifold, invariant to the action
of isometries, and stable to diffeomorphisms for $\lambda$-bandlimited
functions.
