  We present a novel approach for the optical manipulation of neutral atoms in
annular light structures produced by the phenomenon of conical refraction
occurring in biaxial optical crystals. For a beam focused to a plane behind the
crystal, the focal plane exhibits two concentric bright rings enclosing a ring
of null intensity called the Poggendorff ring. We demonstrate both
theoretically and experimentally that the Poggendorff dark ring of conical
refraction is confined in three dimensions by regions of higher intensity. We
derive the positions of the confining intensity maxima and minima and discuss
the application of the Poggendorff ring for trapping ultra-cold atoms using the
repulsive dipole force of blue-detuned light. We give analytical expressions
for the trapping frequencies and potential depths along both the radial and the
axial directions. Finally, we present realistic numerical simulations of the
dynamics of a $^{87}$Rb Bose-Einstein condensate trapped inside the Poggendorff
ring which are in good agreement with corresponding experimental results.
