  Fr\'echet global regression is extended to the context of
Riemannian--manifold--valued bivariate curve data correlated in time.
Specifically, our Fr\'echet predictor is the minimizer of a weighted
$L^{2}$--energy function. We restrict our attention to the case of a compact
and connected Riemannian submanifold of a Euclidean space. Suitable regularity
assumptions, and dispersion restrictions are considered on the manifold
continuous curves defining the state space of the regressor and response
processes. Under stationarity and ergodicity, uniform weak--consistency of the
functional Fr\'echet predictor is proved. A simulated example in the sphere
illustrates the finite--sample--size performance of the proposed
manifold--valued Fr\'echet curve predictor. A real data example is considered,
where the time--varying spherical coordinates of the magnetic field vector are
predicted from the geocentric latitude and longitude of the satellite NASA's
MAGSAT spacecraft.
