What radio pulsars could also be gamma-ray pulsars? This important problem has been discussed and analysed in this paper. The Hardee mechanism of e~+e~- production at the magnetic axis by high energy gamma photons is proved to be very important in understanding the relations between radio pulsars and gamma-ray pulsars. Various physical quantities of gamma-ray pulsar candidates are given. And the possible gamma-ray emissions from the SN 1987A pulsar are also discussed.
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