  We present the relativistic analogue of the Cucker-Smale model with a bonding
force on Riemannian manifold, and study its emergent dynamics. The Cucker-Smale
model serves a prototype example of mechanical flocking models, and it has been
extensively studied from various points of view. Recently, the authors studied
collision avoidance and asymptotic flocking of the Cucker-Smale model with a
bonding force on the Euclidean space. In this paper, we provide an analytical
framework for collision avoidance and asymptotic flocking of the proposed model
on Riemannian manifolds. Our analytical framework is explicitly formulated in
terms of system parameters, initial data and the injectivity radius of the
ambient manifold, and we study how the geometric information of an ambient
manifold can affect the flocking dynamics.
