The rotor core of a synchronous motor or a synchronous generator with a permanent magnet is comprised of a multiplicity of laminated thin iron sheets each having as many segments as the poles. Slits are formed between each adjacent segment, and the magnetic reluctance of the slits is made larger than that between the rotor core and the stator core, thereby minimizing the leakage fluxes within the rotor core. Each segment is required to be prevented from being broken away by centrifugal force generated while the machine is in operation. According to the invention, adjacent segments are connected by a non-magnetic material through the slits. The non-magnetic material is fitted in the recesses formed at both sides of the slit in such a manner as to connect them with each other, each of the recesses being positioned substantially parallel to the circumference of the rotor and having a wider bottom than the opening thereof.