  We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid
$\mathbb{H}^d$ in any dimensions. In a recent work \cite{H-H-K-K-M}, a
first-order aggregation model on the hyperboloid was proposed and its emergent
dynamics was analyzed in terms of initial configuration and system parameters.
In this paper, we are interested in the second-order modeling of Cucker-Smale
flocks on the hyperboloid. For this, we derive our second-order model from the
abstract CS model on complete and smooth Riemannian manifolds by explicitly
calculating the geodesic and parallel transport. Velocity alignment has been
shown by combining general {velocity alignment estimates} for the abstract CS
model on manifolds and verifications of a priori estimate of second derivative
of energy functional. For the two-dimensional case $\mathbb{H}^2$, similar to
the recent result in \cite{A-H-S}, asymptotic flocking admits only two types of
asymptotic scenarios, either convergence to a rest state or a state lying on
the same plane (coplanar state). We also provide several numerical simulations
to illustrate an aforementioned dichotomy on the asymptotic dynamics of the
hyperboloid CS model on $\mathbb{H}^2$.
