A permanent magnet rotating electric machine comprising: a stator including: a stator core having a plurality of teeth; and an armature winding wound around each of the plurality of teeth to configure the multiple phases; and a rotor including: a rotor core; and a plurality of permanent magnets provided in order in a peripheral direction around the rotor core, wherein the rotor is arranged to be spaced apart from the stator with an air gap therebetween, and wherein each of the permanent magnets has a curved surface opposed to the stator and is configured to satisfy the following relationship: 0.65 ≤ Rm * h 1 / W h 1 + g ≤ 1.37 where Rm denotes a radius of curvature of the curved surface, h1 denotes a thickness of a central portion of the permanent magnet in the peripheral direction, W denotes a width of the permanent magnet in the peripheral direction, and g denotes an air gap length of the air gap which is the distance between the center point on the stator opposed surface of the permanent magnet and the top end of the teeth, wherein the armature windings are wound in same phase and in reverse directions around adjacent teeth; further comprising a projection portion provided between adjacent permanent magnets, the projection portion being made of magnetic substance and projecting from the rotor core; wherein the projection portion and each of the permanent magnets are configured to satisfy the following relationships, h 3 / h 2 ≥ 0.38 and h 1 ≥ h 3 where h1 denotes a thickness of the central portion of the permanent magnet in the peripheral direction, h2 denotes a thickness of an end portion of the permanent magnet in the peripheral direction, and h3 denotes a height of the projection portion. a stator core having a plurality of teeth; and an armature winding wound around each of the plurality of teeth to configure the multiple phases; and a rotor including: a rotor core; and a plurality of permanent magnets provided in order in a peripheral direction around the rotor core, wherein the rotor is arranged to be spaced apart from the stator with an air gap therebetween, and wherein each of the permanent magnets has a curved surface opposed to the stator and is configured to satisfy the following relationship: 0.65 ≤ Rm * h 1 / W h 1 + g ≤ 1.37 where Rm denotes a radius of curvature of the curved surface, h1 denotes a thickness of a central portion of the permanent magnet in the peripheral direction, W denotes a width of the permanent magnet in the peripheral direction, and g denotes an air gap length of the air gap which is the distance between the center point on the stator opposed surface of the permanent magnet and the top end of the teeth, wherein the armature windings are wound in same phase and in reverse directions around adjacent teeth; further comprising a projection portion provided between adjacent permanent magnets, the projection portion being made of magnetic substance and projecting from the rotor core; wherein the projection portion and each of the permanent magnets are configured to satisfy the following relationships, h 3 / h 2 ≥ 0.38 and h 1 ≥ h 3 where h1 denotes a thickness of the central portion of the permanent magnet in the peripheral direction, h2 denotes a thickness of an end portion of the permanent magnet in the peripheral direction, and h3 denotes a height of the projection portion. a rotor core; and a plurality of permanent magnets provided in order in a peripheral direction around the rotor core, wherein the rotor is arranged to be spaced apart from the stator with an air gap therebetween, and wherein each of the permanent magnets has a curved surface opposed to the stator and is configured to satisfy the following relationship: 0.65 ≤ Rm * h 1 / W h 1 + g ≤ 1.37 where Rm denotes a radius of curvature of the curved surface, h1 denotes a thickness of a central portion of the permanent magnet in the peripheral direction, W denotes a width of the permanent magnet in the peripheral direction, and g denotes an air gap length of the air gap which is the distance between the center point on the stator opposed surface of the permanent magnet and the top end of the teeth, wherein the armature windings are wound in same phase and in reverse directions around adjacent teeth; further comprising a projection portion provided between adjacent permanent magnets, the projection portion being made of magnetic substance and projecting from the rotor core; wherein the projection portion and each of the permanent magnets are configured to satisfy the following relationships, h 3 / h 2 ≥ 0.38 and h 1 ≥ h 3 where h1 denotes a thickness of the central portion of the permanent magnet in the peripheral direction, h2 denotes a thickness of an end portion of the permanent magnet in the peripheral direction, and h3 denotes a height of the projection portion.