  The Hamiltonian for nanocones with curvature induced spin orbit coupling have
been derived. The effect of curvature induced spin orbit coupling on the
electronic properties of graphitic nanocones is considered. Energy spectra for
different numbers of the pentagonal defects in the tip of the nanocones are
calculated. It was shown that the spin orbit interaction considerably affects
the local density of states of the graphitic nanocone. This influence depends
on the number of defects present at the tip of the nanocone. This property
could be applied in atomic force microscopy for the construction of the probing
tip.
