  Existence of a protected surface state described by a massless Dirac equation
is a defining property of the topological insulator. Though this statement can
be explicitly verified on an idealized flat surface, it remains to be addressed
to what extent it could be general. On a curved surface, the surface Dirac
equation is modified by the spin connection terms. Here, in the light of the
differential geometry, we give a general framework for constructing the surface
Dirac equation starting from the Hamiltonian for bulk topological insulators.
The obtained unified description clarifies the physical meaning of the spin
connection.
