  A massive quantum particle on a two-dimensional curved surface experiences a
surface-geometry induced attractive potential that is characterized by the
radii of curvature at a given point. With bilayer graphene sheets and carbon
nano-ribbons in mind, we obtain the geometric potential V_G for several surface
shapes. Under appropriate conditions that we discuss in detail, this potential
suppresses the local Fermi energy. Therefore, we argue that in zero band-gap
materials with a quadratic band structure, it will create p- and n-type
regions. We discuss the consequences of this result, and suggest that surface
curvature can provide a novel avenue to create p-n junctions and, in general,
to control local electronic properties in bilayer graphene sheets.
