Symmetry restrictions in chirality dependence of physical properties of single wall nanotubes

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We investigate the chirality dependence of physical properties of nanotubes which are wrapped by the planar hexagonal lattice including graphite and boron nitride sheet, and reveal its symmetry origin. The observables under consideration are of scalar, vector and tensor types. These exact chirality dependence obtained are useful to verify the experimental and numerical results and propose accurate empirical formulas. Some important features of physical quantities can also be extracted by only considering the symmetry restrictions without complicated calculations.