Containerless solidification of the undercooled RMnO3 melt was carried out to study the formation of orthorhombic and hexagonal phases under controlled oxygen partial pressure. The o-RMnO3 (R=La to Gd) perovskite with a space group of Pbnm and h-RMnO3 (R=Dy to Lu) with a space group of P6(3)cm were solidified from an undercooled melt at P-O2 = 10(5) Pa. The RMnO3 samples showed the undercooling of 230-380 K at P-O2 = 10(5) Pa. The surface morphologies changed from rough spherical to a smooth faceted planes with a decreasing ionic radius from La (0.1032 nm) to Lu (0.0861 nm). X-ray diffractometry and scanning electron microscopy results showed the existence of o-RMnO3 and h-RMnO3. Thermodynamic stabilities of the as-solidified phases were studied at 10(5) Pa; as a result, the hexagonal phases changed to orthorhombic for the DyMnO3 and HoMnO3 systems after annealing at 1673 K. Based on the thermogravimetric analysis results, oxygen deficiency, bulk composition, and tolerance factor were calculated.