  We model the thermal X-ray profiles of Geminga, Vela and PSR 0656+14, which
have also been detected as gamma-ray pulsars, to constrain the phase space of
obliquity and observer angles required to reproduce the observed X-ray pulsed
fractions and pulse widths. These geometrical constraints derived from the
X-ray light curves are explored for various assumptions about surface
temperature distribution and flux anisotropy caused by the magnetized
atmosphere. We include curved spacetime effects on photon trajectories and
magnetic field. The observed gamma-ray pulse profiles are double peaked with
phase separations of 0.4 - 0.5 between the peaks. Assuming that the gamma-ray
profiles are due to emission in a hollow cone centered on the magnetic pole, we
derive the constraints on the phase space of obliquity and observer angles, for
different gamma-ray beam sizes, required to produce the observed gamma-ray peak
phase separations. We compare the constraints from the X-ray emission to those
derived from the observed gamma-ray pulse profiles, and find that the
overlapping phase space requires both obliquity and observer angles to be
smaller than 20-30 degrees, implying gamma-ray beam opening angles of at most
30-35 degrees.
