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

Protection of the surface states in topological insulators: Berry phase perspective