Active systems on curved geometries are ubiquitous in the living world. In
the presence of curvature orientationally ordered polar flocks are forced to be
inhomogeneous, often requiring the presence of topological defects even in the
steady state due to the constraints imposed by the topology of the underlying
surface. In the presence of spontaneous flow the system additionally supports
long-wavelength propagating sound modes which get gapped by the curvature of
the underlying substrate. We analytically compute the steady state profile of
an active polar flock on a two-sphere and a catenoid, and show that curvature
and active flow together result in symmetry protected topological modes that
get localized to special geodesics on the surface (the equator or the neck
respectively). These modes are the analogue of edge states in electronic
quantum Hall systems and provide unidirectional channels for information
transport in the flock, robust against disorder and backscattering.Comment: 15 pages, 6 figure