  The evolution of spin- and orbital-ordered states has been systematically
investigated for a series of insulating perovskites $R$MnO$_3$
($R$=La,Pr,Nd,...). $R$MnO$_3$ with a large GdFeO$_3$-type distortion is
regarded as a frustrated spin system having ferromagnetic nearest-neighbor and
antiferromagnetic (AF) next-nearest-neighbor (NNN) interactions within a
MnO$_2$ plane. The staggered orbital order associated with the GdFeO$_3$-type
distortion induces the anisotropic NNN interaction, and yields the unique
sinusoidal and $E$-type ("up-up-down-down") AF ordered states in the distorted
perovskites with $e_g^1$ configuration.
