  The low energy excitations of graphene can be described by a massless Dirac
equation in two spacial dimensions. Curved graphene is proposed to be described
by coupling the Dirac equation to the corresponding curved space. This
covariant formalism gives rise to an effective hamiltonian with various extra
terms. Some of them can be put in direct correspondence with more standard
tight binding or elasticity models while others are more difficult to grasp in
standard condensed matter approaches. We discuss this issue, propose models for
singular and regular curvature and describe the physical consequences of the
various proposals.
