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Curvature radiation, like synchrotron radiation, is electromagnetic radiation from charged particles (typically electrons or positrons) traveling at relativistic speeds, their path curved by a magnetic field. In the case of curvature radiation, the particle's curved path is due to its following a magnetic field line that is curved. Both kinds of radiation are polarized and are non-thermal (non-black-body) continuum emissions. (Often, curvature radiation is considered a type of synchrotron radiation.)
Curvature radiation is considered a possible cause of pulsar radio and/or gamma-ray emissions, particularly the beamed radiation resulting in the apparent pulses. As far as I can understand, the strongest outward radiation is that directed out between magnetic field lines that are not returning to the pulsar, i.e., called open magnetic field lines (not open as if they have no end, but reaching elsewhere, with the term closed magnetic field lines indicating lines that loop around locally). The light cylinder (mathematical cylindrical surface at which anything corotating with the pulsar would be moving at the speed of light) forces some lines to be open.