  For a free particle that non-relativistically moves on a curved surface,
there are curvature-induced quantum potentials that significantly influence the
surface quantum states, but the experimental results in topological insulators,
whenever curved or not, indicate no evidence of such a potential, implying that
there does not exist such a quantum potential for the relativistic particles,
constrained on the surface or not. Within the framework of Dirac quantization
scheme, we demonstrate a general result that for a Dirac fermion on a
two-dimensional curved surface of revolution, no curvature-induced quantum
potential is permissible.
