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We study the effect of the curved ripples observed in the free standinggraphene samples on the electronic structure of the system. We model theripples as smooth curved bumps and compute the Green's function of the Diracfermions in the curved surface. Curved regions modify the Fermi velocity thatbecomes a function of the point on the graphene surface and induce energydependent oscillations in the local density of states around the position ofthe bump. The corrections are estimated to be of a few percent of the flatdensity at the typical energies explored in local probes such as scanningtunnel microscopy that should be able to observe the predicted correlation ofthe morphology with the electronics. We discuss the connection of the presentwork with the recent observation of charge anisotropy in graphene and proposethat it can be used as an experimental test of the curvature effects.

Charge inhomogeneities due to smooth ripples in graphene sheets