  We study harmonic and totally invariant measures in a foliated compact
Riemannian manifold isometrically embedded in an Euclidean space. We introduce
geometrical techniques for stochastic calculus in this space. In particular,
using these techniques we can construct explicitely an Stratonovich equation
for the foliated Brownian motion (cf. L. Garnett \cite{LG} and others). We
present a characterization of totally invariant measures in terms of the flow
of diffeomorphisms of associated to this equation. We prove an ergodic formula
for the sum of the Lyapunov exponents in terms of the geometry of the leaves.
