  The metallic surface state of a topological insulator (TI) is not only
topologically protected, but exhibits a remarkable property of inducing an
effective vector potential on curved surfaces. For an electron in the surface
state of a spherical or a cylindrical TI (TI nanoparticle or nanowire) a
pseudo-magnetic monopole or a fictitious solenoid is effectively induced,
encoding the geometry of the system. Here, by taking an example of a hyperbolic
surface we demonstrate that as a consequence of this property stemming from its
active spin degree of freedom, the surface state is by itself topologically
protected.
