  We study the effect of the Dresselhaus spin-orbit interaction on the
electronic states and spin relaxation rates of cylindrical quantum dots defined
on quantum wires having wurtzite lattice structure. The linear and cubic
contributions of the bulk Dresselhaus spin-orbit coupling are taken into
account, along with the influence of a weak external magnetic field. The
previously found analytic solution for the electronic states of cylindrical
quantum dots with zincblende lattice structures with Rashba interaction is
extended to the case of quantum dots with wurtzite lattices. For the electronic
states in InAs dots, we determine the spin texture and the effective g-factor,
which shows a scaling collapse when plotted as a function of an effective
renormalized dot-size dependent spin-orbit coupling strength. The
acoustic-phonon-induced spin relaxation rate is calculated and the transverse
piezoelectric potential is shown to be the dominant one.
