  The spin interaction of a hole confined in a quantum dot with the surrounding
nuclei is described in terms of an effective magnetic field. We show that, in
contrast to the Fermi contact hyperfine interaction for conduction electrons,
the dipole-dipole hyperfine interaction is anisotropic for a hole, for both
pure or mixed hole states. We evaluate the coupling constants of the
hole-nuclear interaction and demonstrate that they are only one order of
magnitude smaller than the coupling constants of the electron-nuclear
interaction. We also study, theoretically, the hole spin dephasing of an
ensemble of quantum dots via the hyperfine interaction in the framework of
frozen fluctuations of the nuclear field, in absence or in presence of an
applied magnetic field. We also discuss experiments which could evidence the
dipole-dipole hyperfine interaction and give information on hole mixing.
