The electronic and structural properties of hexagonal boron nitride (0002) surfaces closed by one and two nanoarches are investigated through first-principles density functional calculations. The surface with one arch is semiconductor whereas the double arch surface presents a metallic behaviour. For the surface with two nanoarches, the level crossing the Fermi energy shows a delocalization along the direction of the nanoarches' axes, defining a one-dimensional channel for electron conduction at the surface. Possible reactive sites on these surfaces, related to the cubic boron nitride growth, are suggested.